SmarterEd

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Equations, SM-Bank 015

A square with side length  \(\large x\)  has an area of \(81\ \text{cm}^2\).

Write an equation and solve it to find the side length.  (2 marks)

Show Answers Only

\(x^2=81\  \ ,\  \  x=9\ \text{cm}\)

Show Worked Solution
\(x^2\) \(=81\)
\(x\) \(=\sqrt{81}\)
\(x\) \(=9\)

 
\(\therefore\ \text{The side length is }9\ \text{cm}\)

Equations, SM-Bank 014

A number  \(\large p\)  is halved and the result is 125.6.

Write an equation and solve it to find the number.  (2 marks)

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\(\dfrac{p}{2}=125.6\  \ ,\  \  p=251.2\)

Show Worked Solution
\(\dfrac{p}{2}\) \(=125.6\)
\(p\) \(=2\times 125.6\)
\(p\) \(=251.2\)

 
\(\therefore\ \text{The number is }251.2\)

Equations, SM-Bank 013

A number  \(\large w\)  is tripled and the result is 141.

Write an equation and solve it to find the number.  (2 marks)

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\(3w=141\  \ ,\  \  w=47\)

Show Worked Solution
\(3w\) \(=141\)
\(w\) \(=\dfrac{141}{3}\)
\(w\) \(=47\)

 
\(\therefore\ \text{The number is }47\)

Equations, SM-Bank 012

Verity and three of her friends won  \(x\) dollars in a lottery. When the money was divided evenly between the four friends they each received \($124\ 500\).

Write an equation and solve it to find out the total amount of their lottery winnings.  (2 marks)

Show Answers Only

\(\dfrac{x}{4}=124\ 500\  \ ,\  \  x=$498\ 000\)

Show Worked Solution
\(\dfrac{x}{4}\) \(=124\ 500\)
\(x\) \(=4\times 124\ 500\)
\(x\) \(=498\ 000\)

 
\(\therefore\ \text{The amount of their total winnings was}\ $498\ 000\)

Equations, SM-Bank 011

Josh is currently \(x\) years old. In \(15\) years he will be 42.

Write an equation and solve it to find Josh's current age.  (2 marks)

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\(x+15=42\  \ ,\  \  x=27\ \text{years old}\)

Show Worked Solution
\(x+15\) \(=42\)
\(x\) \(=42-15\)
\(x\) \(=27\)

 
\(\therefore\ \text{Josh’s current age is}\ 27\ \text{years}\)

Equations, SM-Bank 010

Preston is paid \(x\) dollars per basket of grapes he picks. Yesterday he picked \(8\) baskets and he earned $306.

Write an equation and solve it to find Preston's rate of pay per basket.  (2 marks)

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\(8x=306\  \ ,\  \  x=$38.25\)

Show Worked Solution
\(8x\) \(=306\)
\(x\) \(=\dfrac{306}{8}\)
\(x\) \(=38.25\)

 
\(\therefore\ \text{Preston’s rate of pay per basket is}\ $38.25\)

Equations, SM-Bank 009

Missy is paid \(x\) dollars per hour. Last week she worked \(20\) hours and she earned $350.

Write an equation and solve it to find Missy's hourly rate of pay.  (2 marks)

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\(20x=350\  \ ,\  \  x=$17.50\)

Show Worked Solution
\(20x\) \(=350\)
\(x\) \(=\dfrac{350}{20}\)
\(x\) \(=17.50\)

 
\(\therefore\ \text{Missy’s hourly rate of pay is}\ $17.50\)

Equations, SM-Bank 008

Solve the following one-step equations.

  1. \(s-3=-4\)  (1 mark)

  2. \(c+4=-2\)  (1 mark)

  3. \(-3x=36\)  (1 mark)

  4. \(\dfrac{b}{6}=-4\)  (1 mark)

Show Answers Only

a.    \(s=-1\)

b.    \(c=-6\)

c.    \(x=-12\)

d.    \(b=-24\)

Show Worked Solution
a.    \(s-3\) \(=-4\)
  \(s\) \(=-4+3\)
  \(s\) \(=-1\)

 

b.    \(c+4\) \(=-2\)
  \(c\) \(=-2-4\)
  \(c\) \(=-6\)

 

c.    \(-3x\) \(=36\)
  \(x\) \(=\dfrac{36}{-3}\)
  \(x\) \(=-12\)

 

d.    \(\dfrac{b}{6}\) \(=-4\)
  \(b\) \(=-4\times 6\)
  \(b\) \(=-24\)

Equations, SM-Bank 007

Solve the following one-step equations.

  1. \(x+4=10\)  (1 mark)

  2. \(m-7=2\)  (1 mark)

  3. \(2u=28\)  (1 mark)

  4. \(\dfrac{r}{2}=5\)  (1 mark)

Show Answers Only

a.    \(x=6\)

b.    \(m=9\)

c.    \(u=14\)

d.    \(r=10\)

Show Worked Solution
a.    \(x+4\) \(=10\)
  \(x\) \(=10-4\)
  \(x\) \(=6\)

 

b.    \(m-7\) \(=2\)
  \(m\) \(=2+7\)
  \(m\) \(=9\)

 

c.    \(2u\) \(=28\)
  \(u\) \(=\dfrac{28}{2}\)
  \(u\) \(=14\)

 

d.    \(\dfrac{r}{2}\) \(=5\)
  \(r\) \(=5\times 2\)
  \(r\) \(=10\)

Equations, SM-Bank 006

Jace is paid \(x\) dollars per hour. Last week he worked \(15\) hours and he earned $300.

Write an equation describing his wages for the week.  (2 marks)

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\(15x=300\)

Show Worked Solution

\(15x=300\)

Equations, SM-Bank 004

Write an equation for:

  1. the difference between \(x\) and \(3\) is \(4\). (1 mark)

  2. the product of \(m\) and \(7\) is \(21\). (1 mark)

  3. the sum of \(p\) and \(3\) is doubled and the answer is 8. (1 mark)

  4. half of \(z\) is added to 6 and the result is 12. (1 mark)

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a.    \(x-3=4\)

b.    \(7m=21\)

c.    \(2(p+3)=8\)

d.    \(\dfrac{z}{2}+6=12\)

Show Worked Solution

a.    \(x-3=4\)

b.    \(7m=21\)

c.    \(2(p+3)=8\)

d.    \(\dfrac{z}{2}+6=12\)

Equations, SM-Bank 002 MC

Which of the following equations is not correct?

  1. \(3+2+7=2\times 6\)
  2. \(x+1=2x-1,\ \text{when }x=2\)
  3. \(18-3\times 4=3\times 2\)
  4. \(19-13=3^2\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Checking each option:}\)

\(\text{Option A:}\longrightarrow\) \(3+2+7=2\times 6\ \ \checkmark\)
\(\text{Option B:}\longrightarrow\) \(2+1=2\times 2 -1\ \ \checkmark\)
\(\text{Option C:}\longrightarrow\) \(18-3\times 4=3\times 2\ \ \checkmark\)
\(\text{Option D:}\longrightarrow\) \(19-13\ne 3^2\)

 
\(\Rightarrow D\)

Indices, SM-Bank 101

Simplify  \(2^3\times 5^4\times 2^5\ ÷\  5^2\), giving your answer in simplified index form.  (2 marks)

Show Answers Only

\(2^8\times 5^2\)

Show Worked Solution
\(2^3\times 5^4\times 2^5\ ÷\  5^2\) \(=2^{3+5}\times 5^{4-2}\)
  \(=2^8\times 5^2\)

Indices, SM-Bank 099

Simplify the following, giving your answers in index form.

  1. \((2+3)^0\)  (1 mark)

  2. \(2(4^0)-2\)  (2 marks)

  3. \(3\times 6^0+4\times 2^0\)  (2 marks)

Show Answers Only

a.    \(1\)

b.    \(0\)

b.    \(7\)

Show Worked Solution

a.   \((2+3)^0=5^0=1\)

b.   \(2(4^0)-2=2\times 1-2=0\)

c.   \(3\times 6^0+4\times 2^0=3\times 1+4\times 1=7\)

Indices, SM-Bank 098

Simplify the following, giving your answers in index form.

  1. \(4^0\)  (1 mark)

  2. \(6^0+2^0\)  (2 marks)

  3. \(4+2^0\)  (2 marks)

Show Answers Only

a.    \(1\)

b.    \(2\)

b.    \(5\)

Show Worked Solution

a.   \(4^0=1\)

b.   \(6^0+2^0=1+1=2\)

c.   \(4+2^0=4+1=5\)

Indices, SM-Bank 097

Simplify the following, giving your answers in index form.

  1. \(4^2\ ÷\ 4^2\)  (1 mark)

  2. \(6^3\ ÷\ 6^3\)  (1 mark)

  3. \(12^7\ ÷\ 12^7\)  (1 mark)

Show Answers Only

a.    \(4^0\)

b.    \(6^0\)

b.    \(12^0\)

Show Worked Solution

a.   \(4^2\ ÷\ 4^2=4^{2-2}=4^0\)

b.   \(6^3\ ÷\ 6^3=6^{3-3}=6^0\)

c.   \(12^7\ ÷\ 12^7=12^{7-7}=12^0\)

Indices, SM-Bank 096

Simplify the following, giving your answers in index form.

  1. \((5^2)^2\)  (1 mark)

  2. \((6^3)^4\)  (1 mark)

  3. \((7^4)^5\)  (1 mark)

Show Answers Only

a.    \(5^4\)

b.    \(6^{12}\)

b.    \(7^{20}\)

Show Worked Solution

a.   \((5^2)^2=5^{2\times 2}=5^4\)

b.   \((6^3)^4=6^{3\times 4}=6^{12}\)

c.   \((7^4)^5=7^{4\times 5}=7^{20}\)

Indices, SM-Bank 095

Simplify the following, giving your answers in index form.

  1. \((2^4)^4\)  (1 mark)

  2. \((4^3)^5\)  (1 mark)

  3. \((3^3)^3\)  (1 mark)

Show Answers Only

a.    \(2^{16}\)

b.    \(4^{15}\)

b.    \(3^9\)

Show Worked Solution

a.   \((2^4)^4=2^{4\times 4}=2^{16}\)

b.   \((4^3)^5=4^{3\times 5}=4^{15}\)

c.   \((3^3)^3=3^{3\times 3}=3^9\)

Indices, SM-Bank 094

  1. Write  \((5^2)^4\)  in expanded form.  (2 marks)

  2. Write your answer to (a) in simplified index form.  (1 mark)

Show Answers Only

a.    \((5\times 5)\times (5\times 5)\times (5\times 5)\times (5\times 5)\)

b.    \(5^8\)

Show Worked Solution

a.   \((5^2)^4=(5\times 5)\times (5\times 5)\times (5\times 5)\times (5\times 5)\)
 

b.   \((5\times 5)\times (5\times 5)\times (5\times 5)\times (5\times 5)=5^8\)

Indices, SM-Bank 093

  1. Write  \((2^3)^3\)  in expanded form.  (2 marks)

  2. Write your answer to (a) in simplified index form.  (1 mark)

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a.    \((2\times 2\times 2)\times (2\times 2\times 2)\times (2\times 2\times 2)\)

b.    \(2^9\)

Show Worked Solution

a.   \((2^3)^3=(2\times 2\times 2)\times (2\times 2\times 2)\times (2\times 2\times 2)\)
 

b.   \((2\times 2\times 2)\times (2\times 2\times 2)\times (2\times 2\times 2)=2^9\)

Indices, SM-Bank 092

Find the missing term in the following number sentence.  (1 mark)

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\(2^7\)

Show Worked Solution

\(a^m\ ÷\ a^n=a^{m-n}\)

\(2^n\ ÷\ 2^2\) \(=2^5\)
\(\therefore \ n-2\) \(=5\)
\(n\) \(=7\)

 
\(\therefore \ \text{the missing term is }2^7\)

Indices, SM-Bank 091

Find the missing term in the following number sentence.  (1 mark)

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\(3^{11}\)

Show Worked Solution

\(a^m\ ÷\ a^n=a^{m-n}\)

\(3^n\ ÷\ 3^4\) \(=3^7\)
\(\therefore \ n-4\) \(=7\)
\(n\) \(=11\)

 
\(\therefore \ \text{the missing term is }3^{11}\)

Indices, SM-Bank 090

Simplify the following, giving your answers in index form.

  1. \(\dfrac{2^{16}}{2^9}\)  (1 mark)

  2. \(\dfrac{4^8}{4^3}\)  (1 mark)

  3. \(\dfrac{10^{11}}{10^2}\)  (1 mark)

Show Answers Only

a.    \(2^7\)

b.    \(4^5\)

b.    \(10^9\)

Show Worked Solution

a.   \(\dfrac{2^{16}}{2^9}=2^{16-9}=2^7\)

b.   \(\dfrac{4^8}{4^3}=4^{8-3}=4^5\)

c.   \(\dfrac{10^{11}}{10^2}=10^{11-2}=10^9\)

Indices, SM-Bank 089

Simplify the following, giving your answers in index form.

  1. \(2^8 \ ÷\ 2^4\)  (1 mark)

  2. \(5^{15} \ ÷\ 5^9\)  (1 mark)

  3. \(3^4 \ ÷\ 3\)  (1 mark)

Show Answers Only

a.    \(2^4\)

b.    \(5^6\)

b.    \(3^3\)

Show Worked Solution

a.   \(2^8\ ÷\ 2^4=2^{8-4}=2^4\)

b.   \(5^{15}\ ÷\ 5^9=5^{15-9}=5^6\)

c.   \(3^4\ ÷\ 3^1=3^{4-1}=3^3\)

Indices, SM-Bank 088

  1. Write  \(\dfrac{7^5}{7^2}\)  as a fraction in expanded form.  (2 marks)

  2. Write your answer to (a) in simplified index form.  (1 mark)

Show Answers Only

a.    \(\dfrac{7\times 7\times 7\times 7\times 7}{7\times 7}\)

b.    \(7^3\)

Show Worked Solution

a.   \(\dfrac{7^5}{7^2}=\dfrac{7\times 7\times 7\times 7\times 7}{7\times 7}\)
 

b.   \(\dfrac{7\times 7\times 7\times 7\times 7}{7\times 7}=7^3\)

Indices, SM-Bank 087

  1. Write  \(\dfrac{3^6}{3^4}\)  as a fraction in expanded form.  (2 marks)

  2. Write your answer to (a) in simplified index form.  (1 mark)

Show Answers Only

a.    \(\dfrac{3\times 3\times 3\times 3\times 3\times 3}{3\times 3\times 3\times 3}\)

b.    \(3^2\)

Show Worked Solution

a.   \(\dfrac{3^6}{3^4}=\dfrac{3\times 3\times 3\times 3\times 3\times 3}{3\times 3\times 3\times 3}\)
 

b.   \(\dfrac{3\times 3\times 3\times 3\times 3\times 3}{3\times 3\times 3\times 3}=3^2\)

Indices, SM-Bank 086

Find the missing term in the following number sentence.  (1 mark)

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\(3^7\)

Show Worked Solution

\(a^m\times a^n=a^{m+n}\)

\(3^n\times 3^4\) \(=3^{11}\)
\(\therefore \ n+4\) \(=11\)
\(n\) \(=7\)

 
\(\therefore \ \text{the missing term is }3^7\)

Indices, SM-Bank 085

Find the missing term in the following number sentence.  (1 mark)

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\(2^6\)

Show Worked Solution

\(a^m\times a^n=a^{m+n}\)

\(2^8\times 2^n\) \(=2^{14}\)
\(\therefore \ 8+n\) \(=14\)
\(n\) \(=6\)

 
\(\therefore \ \text{the missing term is }2^6\)

Indices, SM-Bank 084

Find the missing term in the following number sentence.  (1 mark)

Show Answers Only

\(4^5\)

Show Worked Solution

\(a^m\times a^n=a^{m+n}\)

\(4^3\times 4^n\) \(=4^8\)
\(\therefore \ 3+n\) \(=8\)
\(n\) \(=5\)

 
\(\therefore \ \text{the missing term is }4^5\)

Indices, SM-Bank 083

Simplify the following, giving your answers in index form.

  1. \(2^5\times 2^4\times 2\)  (1 mark)

  2. \(4^3\times 4^2\times 4^6\)  (1 mark)

  3. \(3^2\times 3\times 3^3\)  (1 mark)

Show Answers Only

a.    \(2^{10}\)

b.    \(4^{11}\)

b.    \(3^6\)

Show Worked Solution

a.   \(2^5\times 2^4\times 2=2^{5+4+1}=2^{10}\)

b.   \(4^3\times 4^2\times 4^6=4^{3+2+6}=4^{11}\)

c.   \(3^2\times 3^1\times 3^3=3^{2+1+3}=3^6\)

Indices, SM-Bank 082

Simplify the following, giving your answers in index form.

  1. \(5^3\times 5^2\)  (1 mark)

  2. \(7^7\times 7\)  (1 mark)

  3. \(6^4\times 6^3\)  (1 mark)

Show Answers Only

a.    \(5^5\)

b.    \(7^8\)

b.    \(6^7\)

Show Worked Solution

a.   \(5^3\times 5^2=5^{3+2}=5^5\)

b.   \(7^7\times 7^1=7^{7+1}=7^8\)

c.   \(6^4\times 6^3=6^{4+3}=6^7\)

Indices, SM-Bank 081

  1. Write \(2^3\times 2^2\) in expanded form.  (1 mark)

  2. Write your answer to (a) in index form.  (1 mark)

Show Answers Only

a.    \((2\times 2\times 2)\times (2\times 2)\)

b.    \(2^5\)

Show Worked Solution

a.   \(2^3\times 2^2=(2\times 2\times 2)\times (2\times 2)\)

b.   \(2^3\times 2^2=2^5\)

Indices, SM-Banks 080

  1. Write \(3^2\times 3^4\) in expanded form.  (1 mark)

  2. Write your answer to (a) in index form.  (1 mark)

Show Answers Only

a.    \((3\times 3)\times (3\times 3\times 3\times 3)\)

b.    \(3^6\)

Show Worked Solution

a.   \(3^2\times 3^4=(3\times 3)\times (3\times 3\times 3\times 3)\)

b.   \(3^2\times 3^4=3^6\)

Indices, SM-Bank 079

Evaluate  \(3\times\sqrt{81}+\sqrt[3]{27}\times 2\).  (2 marks)

Show Answers Only

\(33\)

Show Worked Solution
\(3\times \sqrt{81}+\sqrt[3]{27}\times 2\) \(=3\times\sqrt{9\times 9}+\sqrt[3]{3\times 3\times 3}\times 2\)
  \(=3\times 9+3\times 2\)
  \(=33\)

Indices, SM-Bank 078

Evaluate \(3\times\sqrt[3]{64}-\sqrt{100}\).  (2 marks)

Show Answers Only

\(2\)

Show Worked Solution
\(3\times \sqrt[3]{64}-\sqrt{100}\) \(=3\times\sqrt[3]{4\times 4\times 4}-\sqrt{10\times 10}\)
  \(=3\times 4-10\)
  \(=2\)

Indices, SM-Bank 075

Find the missing whole number that makes the following number sentence correct.  (2 marks)

Show Answers Only

Show Worked Solution

\(\text{Using trial and error method:}\)

\(\text{Test 1st square number}\ \rightarrow 1\)

\(\text{LHS:}\) \(\ 3\times 1^2+(\sqrt{25}-1)=3\times 1+(5-1)\)
  \(=7\)
\(\text{RHS:}\) \(\ \sqrt{1}\times 9\times 3-5=1\times 27-5\)
  \(=23\)

\(\text{LHS }\ne\text{ RHS}\)
 

\(\text{Test 2nd square number}\ \rightarrow 4\)

\(\text{LHS:}\) \(\ 3\times 4^2+(\sqrt{25}-4)=3\times 16+(5-4)\)
  \(=49\)
\(\text{RHS:}\) \(\ \sqrt{4}\times 9\times 3-5=2\times 27-5\)
  \(=49\)

\(\text{LHS }=\text{ RHS}\)

\(\therefore \ \)

 

Indices, SM-Bank 074 MC

Between which two number does \(\sqrt{70}\)  lie?

  1. \(5\ \text{and }6\)
  2. \(6\ \text{and }7\)
  3. \(7\ \text{and }8\)
  4. \(8\ \text{and }9\)
Show Answers Only

\(D\)

Show Worked Solution
\(\text{Consider Option D:}\) \(\rightarrow\ \sqrt{64}=8\)
  \(\rightarrow\ \sqrt{81}=9\)

 

\(\therefore\ \sqrt{70}\ \text{lies between }\sqrt{64} \text{ and }\sqrt{81}\)

\(\therefore\ \sqrt{70}\ \text{lies between }8 \text{ and }9\)

\(\Rightarrow D\)

Indices, SM-Bank 073 MC

Between which two number does \(\sqrt{30}\) lie?

  1. \(3\ \text{and }4\)
  2. \(4\ \text{and }5\)
  3. \(5\ \text{and }6\)
  4. \(6\ \text{and }7\)
Show Answers Only

\(C\)

Show Worked Solution
\(\text{Consider Option C:}\) \(\rightarrow\ \sqrt{25}=5\)
  \(\rightarrow\ \sqrt{36}=6\)

 

\(\therefore\ \sqrt{30}\ \text{lies between }\sqrt{25} \text{ and }\sqrt{36}\)

\(\therefore\ \sqrt{30}\ \text{lies between }5 \text{ and }6\)

 
\(\Rightarrow C\)

Indices, SM-Bank 072

Show that  \(\sqrt{9\times 4}=\sqrt{9}\times \sqrt{4}\).  (2 marks)

Show Answers Only

\(\text{See worked solution}\)

Show Worked Solution
\(\text{LHS}:\sqrt{9\times 4}\) \(=\sqrt{ 3\times 3\times 2\times 2}\)
  \(=\sqrt{ 6\times 6}\)
  \(=6\)

 

\(\text{RHS}:\sqrt{9}\times \sqrt{4}\) \(=3\times 2\)
  \(=6\)

\(\therefore\ \text{LHS}\ =\ \text{RHS}\)

\(\therefore\ \sqrt{9\times 4}=\sqrt{9}\times \sqrt{4}\)

Indices, SM-Bank 071

Show that  \(\sqrt{25\times 16}=\sqrt{25}\times \sqrt{16}\).  (2 marks)

Show Answers Only

\(\text{See worked solution}\)

Show Worked Solution
\(\text{LHS}:\sqrt{25\times 16}\) \(=\sqrt{ 5\times 5\times 4\times 4}\)
  \(=\sqrt{ 20\times 20}\)
  \(=20\)

 

\(\text{RHS}:\sqrt{25}\times \sqrt{16}\) \(=5\times 4\)
  \(=20\)

\(\therefore\ \text{LHS}\ =\ \text{RHS}\)

\(\therefore\ \sqrt{25\times 16}=\sqrt{25}\times \sqrt{16}\)

Indices, SM-Bank 070

Show that  \(\sqrt{225}=\sqrt{25}\times \sqrt{9}\).  (2 marks)

Show Answers Only

\(\text{See worked solution}\)

Show Worked Solution
\(\text{LHS}:\sqrt{225}\) \(=\sqrt{ 5\times 45}\)
  \(=\sqrt{ 5\times 5\times 9}\)
  \(=\sqrt{ 5\times 5\times 3\times 3}\)
  \(=\sqrt{ 15\times 15}\)
  \(=15\)

 

\(\text{RHS}:\sqrt{25}\times \sqrt{9}\) \(=5\times 3\)
  \(=15\)

\(\therefore\ \text{LHS}\ =\ \text{RHS}\)

\(\therefore\ \sqrt{225}=\sqrt{25}\times \sqrt{9}\)

Indices, SM-Bank 069

Show that  \(\sqrt{144}=\sqrt{36}\times \sqrt{4}\).  (2 marks)

Show Answers Only

\(\text{See worked solution}\)

Show Worked Solution
\(\text{LHS}:\sqrt{144}\) \(=\sqrt{ 12\times 12}\)
  \(=12\)

 

\(\text{RHS}:\sqrt{36}\times \sqrt{4}\) \(=6\times 2\)
  \(=12\)

\(\therefore\ \text{LHS}\ =\ \text{RHS}\)

\(\therefore\ \sqrt{144}=\sqrt{36}\times \sqrt{4}\)

Indices, SM-Bank 068 MC

Given that  \(12^2=144\), then \(\sqrt{144}=\) ?

  1. \(288\)
  2. \(72\)
  3. \(12\)
  4. \(6\)
Show Answers Only

\(C\)

Show Worked Solution

\(144=12\times 12\ \ \text{(Given)}\)

\(\therefore \sqrt{144}\) \(=\sqrt{ 12\times 12}\)
  \(=12\)

 
\(\Rightarrow C\)

Indices, SM-Bank 067 MC

Given that  \(17^2=289\), then \(\sqrt{289}=\) ?

  1. \(8.5\)
  2. \(13.5\)
  3. \(17\)
  4. \(578\)
Show Answers Only

\(C\)

Show Worked Solution

\(289=17\times 17\ \ \text{(Given)}\)

\(\therefore \sqrt{289}\) \(=\sqrt{ 17\times 17}\)
  \(=17\)

 
\(\Rightarrow C\)

Indices, SM-Bank 066 MC

Given that  \(21^2=441\), then \(\sqrt{441}=\) ?

  1. \(21\)
  2. \(42\)
  3. \(420\)
  4. \(194\ 481\)
Show Answers Only

\(A\)

Show Worked Solution

\(441=21\times 21\ \ \text{(Given)}\)

\(\therefore \sqrt{441}\) \(=\sqrt{ 21\times 21}\)
  \(=21\)

 
\(\Rightarrow A\)

Indices, SM-Bank 065 MC

Given that  \(4^3=64\), then \(\sqrt[3]{64}=\) ?

  1. \(2\)
  2. \(4\)
  3. \(8\)
  4. \(21.3\)
Show Answers Only

\(B\)

Show Worked Solution

\(64=4\times 4\times 4\ \ \text{(Given)}\)

\(\therefore \sqrt[3]{64}\) \(=\sqrt[3]{ 4\times 4\times 4}\)
  \(=4\)

 
\(\Rightarrow B\)

Indices, SM-Bank 064 MC

Given that  \(8^3=512\), then \(\sqrt[3]{512}=\) ?

  1. \(8\)
  2. \(23\)
  3. \(128\)
  4. \(171\)
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\(A\)

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\(512=8\times 8\times 8\ \ \text{(Given)}\)

\(\therefore \sqrt[3]{512}\) \(=\sqrt[3]{ 8\times 8\times 8}\)
  \(=8\)

 
\(\Rightarrow A\)

Indices, SM-Bank 063 MC

Given that  \(5^3=125\), then \(\sqrt[3]{125}=\) ?

  1. \(62.5\)
  2. \(41.7\)
  3. \(11.2\)
  4. \(5\)
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\(D\)

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\(125=5\times 5\times 5\ \ \text{(Given)}\)

\(\therefore \sqrt[3]{125}\) \(=\sqrt[3]{ 5\times 5\times 5}\)
  \(=5\)

 
\(\Rightarrow D\)

Indices, SM-Bank 062

  1. Write 900 as a product of its prime factors.  (2 marks)

  2. Hence find \(\sqrt{900}\).  (2 marks)

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a.    \(2\times 2\times 3\times 3\times 5\times 5\)

b.    \(30\)

Show Worked Solution
a.    \(900\) \(=9\times 100\)
    \(=3\times 3\times 10\times 10\)
    \(=3\times 3\times 2\times 5\times 2\times 5\)
    \(=2\times 2\times 3\times 3\times 5\times 5\)

 

b.    \(\sqrt{900}\) \(=\sqrt{2\times 2\times 3\times 3\times 5\times 5}\)
    \(=\sqrt{(2\times 3\times 5)\times (2\times 3\times 5)}\)
    \(=\sqrt{30\times 30}\)
    \(=30\)

Indices, SM-Bank 061

  1. Write 1024 as a product of its prime factors.  (2 marks)

  2. Hence find \(\sqrt{1024}\).  (2 marks)

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a.    \(2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)

b.    \(32\)

Show Worked Solution
a.    \(1024\) \(=2\times 512\)
    \(=2\times 2\times 256\)
    \(=2\times 2\times 2\times 128\)
    \(=2\times 2\times 2\times 2\times 64\)
    \(=2\times 2\times 2\times 2\times 8\times 8\)
    \(=2\times 2\times 2\times 2\times 2\times 4\times 2\times 4\)
    \(=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)

 

b.    \(\sqrt{1024}\) \(=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}\)
    \(=\sqrt{(2\times 2\times 2\times 2\times 2)\times (2\times 2\times 2\times 2\times 2)}\)
    \(=\sqrt{32\times 32}\)
    \(=32\)

Indices, SM-Bank 060

  1. Write 324 as a product of its prime factors.  (2 marks)

  2. Hence find \(\sqrt{324}\).  (2 marks)

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a.    \(2\times 2\times 3\times 3\times 3\times 3\)

b.    \(18\)

Show Worked Solution
a.    \(324\) \(=2\times 162\)
    \(=2\times 2\times 81\)
    \(=2\times 2\times 9\times 9\)
    \(=2\times 2\times 3\times 3\times 3\times 3\)

 

b.    \(\sqrt{324}\) \(=\sqrt{2\times 2\times 3\times 3\times 3\times 3}\)
    \(=\sqrt{(2\times 3\times 3)\times (2\times 3\times 3)}\)
    \(=\sqrt{18\times 18}\)
    \(=18\)

Indices, SM-Bank 059

  1. Write 256 as a product of its prime factors.  (2 marks)

  2. Hence find \(\sqrt{256}\).  (2 marks)

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a.    \(2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)

b.    \(16\)

Show Worked Solution
a.    \(256\) \(=2\times 128\)
    \(=2\times 2\times 64\)
    \(=2\times 2\times 2\times 32\)
    \(=2\times 2\times 2\times 2\times 16\)
    \(=2\times 2\times 2\times 2\times 2\times 8\)
    \(=2\times 2\times 2\times 2\times 2\times 2\times 4\)
    \(=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\)

 

b.    \(\sqrt{256}\) \(=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}\)
    \(=\sqrt{(2\times 2\times 2\times 2)\times (2\times 2\times 2\times 2)}\)
    \(=\sqrt{16\times 16}\)
    \(=16\)