Equations

Equations, SM-Bank 069

Find the value of $\large c$ in the formula $c^2=a^2+b^2$ given $a=12$ and $b=14$. Assume $\large c$ is positive and give your answer correct to 2 decimal places. (2 marks)

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$c\approx 18.44$

Show Worked Solution

$c^2$	$=a^2+b^2$
$c^2$	$=12^2+14^2$
$c^2$	$=144+196$
$\sqrt{c^2}$	$=\sqrt{340}$
$c$	$=18.4390\ldots$
	$\approx 18.44$

Equations, SM-Bank 068

Find the value of $\large c$ in the formula $c^2=a^2+b^2$, given $a=7$ and $b=24$. Assume $\large c$ is positive. (2 marks)

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$c=25$

Show Worked Solution

$c^2$	$=a^2+b^2$
$c^2$	$=7^2+24^2$
$c^2$	$=49+576$
$\sqrt{c^2}$	$=\sqrt{625}$
$c$	$=25$

Equations, SM-Bank 067

Find the value of $\large r$ in the formula $A=\pi r^2$ given $A=10$. Assume $\large r$ is positive and give your answer correct to 1 decimal place. (2 marks)

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$r\approx 1.8$

Show Worked Solution

$A$	$=\pi r^2$
$\pi r^2$	$=10$
$r^2$	$=\dfrac{10}{\pi}$
$\sqrt{r^2}$	$=\sqrt{\dfrac{10}{\pi}}$
$r$	$=1.784\ldots$
	$\approx 1.8\ (1\text{ d.p.})$

Equations, SM-Bank 066

Solve the quadratic equation $x^2+3=147$ for $x<0$. (2 marks)

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$x=-12$

Show Worked Solution

$x^2+3$	$=147$
$x^2$	$=147-3$
$x^2$	$=144$
$\sqrt{x^2}$	$=\sqrt{144}$
$x$	$=\pm12$

$\therefore\ \text{Since}\ x<0\ x=-12$

Equations, SM-Bank 065

Solve the quadratic equation $x^2-1=48$ for $x>0$. (2 marks)

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$x=7$

Show Worked Solution

$x^2-1$	$=48$
$x^2$	$=48+1$
$x^2$	$=49$
$\sqrt{x^2}$	$=\sqrt{49}$
$x$	$=\pm7$

$\therefore\ \text{Since}\ x>0\ \ x=7$

Equations, SM-Bank 064

A square has an area of $121\ \text{cm}^2$.

Find the side length of the square. (2 marks)

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Find the perimeter of the square. (2 marks)

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a. $11\ \text{cm}$

b. $44\ \text{cm}$

Show Worked Solution

a.	$A$	$=s^2$
	$A$	$=121\ \ \text{(given)}$
	$\therefore\ s^2$	$=121$
	$\sqrt{s^2}$	$=\sqrt{121}$
	$s$	$=11$

$\text{Side length}=11\ \text{cm}$

b.	$\text{Perimeter}$	$=4\times s$
		$=4\times 11$
		$=44$

$\text{Perimeter}=44\ \text{cm}$

Equations, SM-Bank 063

A square has an area of $36\ \text{m}^2$.

Find the side length of the square. (2 marks)

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Find the perimeter of the square. (2 marks)

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a. $6\ \text{m}$

b. $24\ \text{m}$

Show Worked Solution

a.	$A$	$=s^2$
	$A$	$=36\ \ \text{(given)}$
	$\therefore\ s^2$	$=36$
	$\sqrt{s^2}$	$=\sqrt{36}$
	$s$	$=6$

$\text{Side length}=6\ \text{m}$

b.	$\text{Perimeter}$	$=4\times s$
		$=4\times 6$
		$=24$

$\text{Perimeter}=24\ \text{m}$

Equations, SM-Bank 062

Solve, giving all solutions correct to 1 decimal place.

$x^2=8$ (2 marks)

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$x^2=323$ (2 marks)

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a. $x=\pm 2.8$

b. $x=\pm 18.0$

Show Worked Solution

a.	$x^2$	$=8$
	$\sqrt{x^2}$	$=\pm\sqrt{8}$
	$x$	$=\pm 2.828…\ =\pm 2.8$

b.	$x^2$	$=323$
	$\sqrt{x^2}$	$=\pm\sqrt{323}$
	$x$	$=\pm 17.972…\ =\pm 18.0$

Equations, SM-Bank 061

Solve, giving all solutions.

$x^2=25$ (2 marks)

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$x^2=289$ (2 marks)

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a. $x=\pm 5$

b. $x=\pm 17$

Show Worked Solution

a.	$x^2$	$=25$
	$\sqrt{x^2}$	$=\pm\sqrt{25}$
	$x$	$=\pm 5$

b.	$x^2$	$=289$
	$\sqrt{x^2}$	$=\pm\sqrt{289}$
	$x$	$=\pm 17$

Equations, SM-Bank 060

Show that $x^2=64$ has 2 solutions. (2 marks)

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$\text{See worked solutions}$

Show Worked Solution

$8^2=8\times 8=64\ \ \therefore \ x=8\ \text{is a solution.}$

$(-8)^2=-8\times -8=64\ \ \therefore \ x=-8\ \text{is a solution.}$

$\therefore x=8\ \text{and }x=-8\ \text{are both solutions of }x^2=64$

Equations, SM-Bank 059

Show that $x^2=100$ has 2 solutions. (2 marks)

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$\text{See worked solutions}$

Show Worked Solution

$10^2=10\times 10=100\ \ \therefore \ x=10\ \text{is a solution.}$

$(-10)^2=-10\times -10=100\ \ \therefore \ x=-10\ \text{is a solution.}$

$\therefore x=10\ \text{and }x=-10\ \text{are both solutions of }x^2=100$

Equations, SM-Bank 058

Show that $x^2=9$ has 2 solutions. (2 marks)

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$\text{See worked solutions}$

Show Worked Solution

$3^2=3\times 3=9\ \ \therefore \ x=3\ \text{is a solution.}$

$(-3)^2=-3\times -3=9\ \ \therefore \ x=-3\ \text{is a solution.}$

$\therefore x=3\ \text{and }x=-3\ \text{are both solutions of }x^2=9$

Equations, SM-Bank 057 MC

Which of the following is not equal to $16$?

$8^2$
$(-4)^2$
$4\times 4$
$2^4$

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$A$

Show Worked Solution

$\text{Option A: }\ \ $	$8^2=8\times 8=64\ne 16$
$\text{Option B: }\ \ $	$(-4)^2=-4\times -4=16\ \ \checkmark$
$\text{Option C: }\ \ $	$4\times 4=16\ \ \checkmark$
$\text{Option D: }\ \ $	$2^4=2\times 2\times 2\times 2=16\ \ \checkmark$

$\Rightarrow A$

Equations, SM-Bank 056 MC

Which of the following is not equal to $9$?

$-3\times -3$
$4.5^2$
$\sqrt{81}$
$3^2$

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$B$

Show Worked Solution

$\text{Option A: }\ \ $	$-3\times -3=9\ \ \checkmark$
$\text{Option B: }\ \ $	$4.5^2=20.25\ne 9$
$\text{Option C: }\ \ $	$\sqrt{81}=9\ \ \checkmark$
$\text{Option D: }\ \ $	$3^2=9\ \ \checkmark$

$\Rightarrow B$

Equations, SM-Bank 056

The formula for converting degrees Celsius to Fahrenheit is $F=\dfrac{9C}{5}+32$.

Find $F$ is $C=35$. (2 marks)

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Find $C$ is $F=68$. (2 marks)

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a. $F=95$

b. $C=20$

Show Worked Solution

a.	$F$	$=\dfrac{9C}{5}+32$
	$F$	$=\dfrac{9\times 35}{5}+32$
	$F$	$=\dfrac{315}{5}+32$
	$F$	$=63+32=95$

b.	$F$	$=\dfrac{9C}{5}+32$
	$68$	$=\dfrac{9C}{5}+32$
	$\dfrac{9C}{5}$	$=68-32$
	$\dfrac{9C}{5}$	$=36$
	$9C$	$=36\times 5$
	$9C$	$=180$
	$C$	$=\dfrac{180}{9}=20$

Equations, SM-Bank 055

Solve $2(x+3)=15$. (2 marks)

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$x=4.5$

Show Worked Solution

$2(x+3)$	$=15$
$2\times x+2\times 3$	$=15$
$2x+6$	$=15$
$2x$	$=9$
$x$	$=\dfrac{9}{2}$
$x$	$=4.5$

Equations, SM-Bank 054

Solve $3(x-1)=24$. (2 marks)

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$x=9$

Show Worked Solution

$3(x-1)$	$=24$
$3\times x+3\times -1$	$=24$
$3x-3$	$=24$
$3x$	$=27$
$x$	$=\dfrac{27}{3}$
$x$	$=9$

Equations, SM-Bank 053

Write an algebraic equation for the perimeter of the rectangle below and use it to calculate the value of $x$ given the perimeter is $62$. (2 marks)

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$x=3$

Show Worked Solution

$P=2l+2w$

$62$	$=2(7x+1)+2\times 3x$
$62$	$=2\times 7x+2\times 1 +6x$
$62$	$=14x+2 +6x$
$20x+2$	$=62$
$20x$	$=60$
$x$	$=3$

Equations, SM-Bank 052

An isosceles triangle has a perimeter of $46$ and its base is 12. Find the length of its equal sides. (2 marks)

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$l=17$

Show Worked Solution

$P$	$=2l+b$
$46$	$=2l+12$
$2l$	$=34$
$l$	$=\dfrac{34}{2}$
$l$	$=17$

Equations, SM-Bank 051

A rectangle has a length of $12$ and its area is 96. Find its width. (2 marks)

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$w=8$

Show Worked Solution

$A$	$=l\times w$
$96$	$=12\times w$
$12w$	$=96$
$w$	$=\dfrac{96}{12}$
$w$	$=8$

Equations, SM-Bank 050

Find the value of $c$ in the formula $c=\sqrt{a^2+b^2}$ if $a=12$ and $b=5$. (2 marks)

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$c=13$

Show Worked Solution

$c$	$=\sqrt{a^2+b^2}$
$c$	$=\sqrt{12^2+5^2}$
$c$	$=\sqrt{144+25}$
$c$	$=\sqrt{169}$
$c$	$=13$

Equations, SM-Bank 049

Find the value of $a$ in the formula $y=ax^2$ if $y=32$ and $x=4$. (2 marks)

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$a=2$

Show Worked Solution

$y$	$=ax^2$
$32$	$=a\times 4^2 $
$16a$	$=32$
$a$	$=2$

Equations, SM-Bank 048

Solve $\dfrac{2n+3}{2}=-1$. (2 marks)

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$n=-2\dfrac{1}{2}$

Show Worked Solution

$\dfrac{2n+3}{2}$	$=-1$
$2n+3$	$=-1\times 2$
$2n+3$	$=-2$
$2n$	$=-5$
$n$	$=\dfrac{-5}{2}$
$n$	$=-2\dfrac{1}{2}$

Equations, SM-Bank 047

Solve $\dfrac{3x}{5}-8=1$. (2 marks)

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$x=15$

Show Worked Solution

$\dfrac{3x}{5}-8$	$=1$
$\dfrac{3x}{5}$	$=1+8$
$\dfrac{3x}{5}$	$=9$
$3x$	$=9\times 5$
$3x$	$=45$
$x$	$=15$

Equations, SM-Bank 046

Solve $\dfrac{2x}{3}=-8$. (2 marks)

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$x=-12$

Show Worked Solution

$\dfrac{2x}{3}$	$=-8$
$2x$	$=-8\times 3$
$2x$	$=-24$
$x$	$=-12$

Equations, SM-Bank 045

Find the value of $L$ in the formula $P=2L+2W$ if $P=42$ and $W=3$. (2 marks)

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$L=18$

Show Worked Solution

$P$	$=2L+2W$
$42$	$=2L+2\times 3$
$42$	$=2L+6$
$2L$	$=36$
$L$	$=18$

Equations, SM-Bank 044

Find the value of $A$ in the formula $A=\dfrac{h}{2}(a+b)$ if $h=8$, $a=7$ and $b=3$. (2 marks)

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$A=40$

Show Worked Solution

$A$	$=\dfrac{h}{2}(a+b)$
$A$	$=\dfrac{8}{2}(7+3)$
$A$	$=4\times 10$
$A$	$=40$

Equations, SM-Bank 043

Find the value of $y$ in the formula $y=ax+b$ if $a=4$, $x=3$ and $b=5$. (2 marks)

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$y=17$

Show Worked Solution

$y$	$=ax+b$
$y$	$=4\times 3+5$
$y$	$=17$

Equations, SM-Bank 042

Find the value of $A$ in the formula $A=\dfrac{1}{2}bh$ if $b=32$ and $h=10$. (2 marks)

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$A=160$

Show Worked Solution

$A$	$=\dfrac{1}{2}bh$
$A$	$=\dfrac{1}{2}\times 32\times 10$
$A$	$=160$

Equations, SM-Bank 040

Find the value of $a$ in the formula $2a+3b=c$ if $b=2$ and $c=10$. (2 marks)

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$a=2$

Show Worked Solution

$2a+3b$	$=c$
$2a+3\times 2$	$=10$
$2a+6$	$=10$
$2a$	$=4$
$a$	$=2$

Equations, SM-Bank 041

Find the value of $h$ in the formula $V=Ah$ if $V=112$, and $A=7$. (2 marks)

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$h=16$

Show Worked Solution

$V$	$=Ah$
$112$	$=7h$
$h$	$=\dfrac{112}{7}$
$h$	$=16$

Equations, SM-Bank 039

Solve the equation $\dfrac{2x}{7}=1$. (2 marks)

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$x=3\dfrac{1}{2}$

Show Worked Solution

$\dfrac{2x}{7}$	$=1$
$2x$	$=1\times 7$
$2x$	$=7$
$x$	$=\dfrac{7}{2}=3\dfrac{1}{2}$

Equations, SM-Bank 038

Solve the equation $\dfrac{5x}{3}=1$. (2 marks)

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$x=\dfrac{3}{5}$

Show Worked Solution

$\dfrac{5x}{3}$	$=1$
$5x$	$=1\times 3$
$5x$	$=3$
$x$	$=\dfrac{3}{5}$

Equations, SM-Bank 37

Solve the equation $\dfrac{3x}{4}=9$. (2 marks)

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$x=12$

Show Worked Solution

$\dfrac{3x}{4}$	$=9$
$3x$	$=9\times 4$
$3x$	$=36$
$x$	$=12$

Equations, SM-Bank 036

Solve the equation $\dfrac{2x}{3}=10$. (2 marks)

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$x=15$

Show Worked Solution

$\dfrac{2x}{3}$	$=10$
$2x$	$=10\times 3$
$2x$	$=30$
$x$	$=15$

Equations, SM-Bank 035

Two consecutive integers have a sum of 147.

Given the first number is $x$, write an algebraic equation to represent this information. (2 marks)

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Solve your equation algebraically to find the two numbers. (2 marks)

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a. $2x+1=147$

b. $73 , 74$

Show Worked Solution

a. $\text{Given the 1st number is}\ x\text{, the 2nd number is }x+1.$

$\therefore\ \text{Equation is:}$

$x+(x+1)$	$=147$
$2x+1$	$=147$

b.	$2x+1$	$=147$
	$2x$	$=146$
	$x$	$=73$

$\therefore\ \text{Numbers are }73\ \text{and }74.$

Equations, SM-Bank 034

Two consecutive integers have a sum of 25.

Given the first number is $x$, write an algebraic equation to represent this information. (2 marks)

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Solve your equation algebraically to find the two numbers. (2 marks)

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a. $2x+1=25$

a. $12 , 13$

Show Worked Solution

a. $\text{Given the 1st number is}\ x\text{, the 2nd number is }x+1.$

$\therefore\ \text{Equation is:}$

$x+(x+1)$	$=25$
$2x+1$	$=25$

b.	$2x+1$	$=25$
	$2x$	$=24$
	$x$	$=12$

$\therefore\ \text{Numbers are }12\ \text{and }13.$

Equations, SM-Bank 033

Find the value of $t$ in the formula $v=u+at$ if $v=10$, $u=3$ and $a=2$. (2 marks)

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$t=3.5$

Show Worked Solution

$v$	$=u+at$
$10$	$=3+2t$
$2t$	$=10-3$
$2t$	$=7$
$t$	$=3.5$

Equations, SM-Bank 032

Verify that $x=0.3$ is a solution of the equation $8x+0.5=2.9$. (2 marks)

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$\text{See worked solution}$

Show Worked Solution

$\text{When}\ x=7$

$LHS$	$=8x+0.5$
	$=8\times 0.3+0.5$
	$=2.4+0.5=2.9$
	$=RHS$

$\therefore\ x=0.3\ \text{ is a solution}$

Equations, SM-Bank 031

Verify that $x=7$ is a solution of the equation $\dfrac{x-3}{2}=2$. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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$\text{See worked solution}$

Show Worked Solution

$\text{When}\ x=7$

$LHS$	$=\dfrac{x-3}{2}$
	$=\dfrac{7-3}{2}$
	$=\dfrac{4}{2}=2$
	$=RHS$

$\therefore\ x=7\ \text{ is a solution}$

Equations, SM-Bank 030

Verify that $x=\dfrac{3}{4}$ is a solution of the equation $4x-5=-2$. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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$\text{See worked solution}$

Show Worked Solution

$\text{When}\ x=\dfrac{3}{4}$

$LHS$	$=4x-5$
	$=4\times \dfrac{3}{4}-5$
	$=3-5=-2$
	$=RHS$

$\therefore\ x=\dfrac{3}{4}\ \text{ is a solution}$

Equations, SM-Bank 029

Verify that $x=1.5$ is a solution of the equation $\dfrac{2x}{3}+3=4$. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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$\text{See worked solution}$

Show Worked Solution

$\text{When}\ x=1.5$

$LHS$	$=\dfrac{2x}{3}+3$
	$=\dfrac{2\times 1.5}{3}+3$
	$=1+3=4$
	$=RHS$

$\therefore\ x=1.5\ \text{ is a solution}$

Equations, SM-Bank 028

Verify that $x=2$ is a solution of the equation $2x+3=7$. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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$\text{See worked solution}$

Show Worked Solution

$\text{When}\ x=2$

$LHS$	$=2x+3$
	$=2\times 2 +3$
	$=7$
	$=RHS$

$\therefore\ x=2\ \text{ is a solution}$

Equations, SM-Bank 027

Solve $2x+3=4x$. (2 marks)

Show Answers Only

$x=\dfrac{3}{2}$

Show Worked Solution

$2x+3$	$=4x$
$3$	$=4x-2x$
$3$	$=2x$
$2x$	$=3$
$x$	$=\dfrac{3}{2}$

Equations, SM-Bank 026

Solve $\dfrac{x+4}{3}=2$. (2 marks)

Show Answers Only

$x=2$

Show Worked Solution

$\dfrac{x+4}{3}$	$=2$
$x+4$	$=2\times 3$
$x+4$	$=6$
$x$	$=6-4$
$x$	$=2$

Equations, SM-Bank 025

$3$ is subtracted from a quarter of $x$ and the result is $-\dfrac{1}{2}$.

Write an equation and solve it algebraically to find the value of $x$. (3 marks)

Show Answers Only

$x=10$

Show Worked Solution

$\dfrac{x}{4}-3$	$=-\dfrac{1}{2}$
$\dfrac{x}{4}$	$=-\dfrac{1}{2}+3$
$\dfrac{x}{4}$	$=2\dfrac{1}{2}$
$x$	$=4\times 2\dfrac{1}{2}$
$x$	$=10$

Equations, SM-Bank 024

Solve $4c-5.4=-7$ (2 marks)

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$c=-0.4$

Show Worked Solution

$4c-5.4$	$=-7$
$4c$	$=-7+5.4$
$4c$	$=-1.6$
$c$	$=\dfrac{-1.6}{4}$
$c$	$=-0.4$

Equations, SM-Bank 023

Solve $10b-3=-2$ (2 marks)

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$b=0.1$

Show Worked Solution

$10b-3$	$=-2$
$10b$	$=-2+3$
$10b$	$=1$
$b$	$=\dfrac{1}{10}$
$b$	$=0.1$

Equations, SM-Bank 022

Solve $\dfrac{q-4}{2}=6$ (2 marks)

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$q=16$

Show Worked Solution

$\dfrac{q-4}{2}$	$=6$
$q-4$	$=6\times 2$
$q-4$	$=12$
$q$	$=12+4$
$q$	$=16$

Equations, SM-Bank 021

Solve $\dfrac{x+1}{3}=-4$ (2 marks)

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$x=-13$

Show Worked Solution

$\dfrac{x+1}{3}$	$=-4$
$x+1$	$=-4\times 3$
$x+1$	$=-12$
$x$	$=-12-1$
$x$	$=-13$

Equations, SM-Bank 020

Solve $8-\dfrac{x}{9}=-1$ (2 marks)

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$x=81$

Show Worked Solution

$8-\dfrac{x}{9}$	$=-1$
$\dfrac{-x}{9}$	$=-1-8$
$\dfrac{-x}{9}$	$=-9$
$-x$	$=-9\times 9$
$-x$	$=-81$
$x$	$=81$

Equations, SM-Bank 019

Solve $\dfrac{g}{4}+2=7$ (2 marks)

Show Answers Only

$g=20$

Show Worked Solution

$\dfrac{g}{4}+2$	$=7$
$\dfrac{g}{4}$	$=7-2$
$\dfrac{g}{4}$	$=5$
$g$	$=5\times 4$
$g$	$=20$

Equation, SM-Bank 018

Solve $10-7y=-11$ (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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$y=3$

Show Worked Solution

$10-7y$	$=-11$
$-7y$	$=-11-10$
$-7y$	$=-21$
$y$	$=\dfrac{-21}{-7}$
$y$	$=3$

Equations, SM-Bank 017

Solve $3m-8=-26$ (2 marks)

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$m=-6$

Show Worked Solution

$3m-8$	$=-26$
$3m$	$=-26+8$
$3m$	$=-18$
$m$	$=\dfrac{-18}{3}$
$m$	$=-6$

Equations, SM-Bank 016

Solve $2x+3=9$ (2 marks)

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$x=3$

Show Worked Solution

$2x+3$	$=9$
$2x$	$=9-3$
$2x$	$=6$
$x$	$=\dfrac{6}{2}$
$x$	$=3$

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)

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$x^2=81\ \ ,\ \ x=9\ \text{cm}$

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$x^2$	$=81$
$x$	$=\sqrt{81}$
$x$	$=9$

$\therefore\ \text{The side length is }9\ \text{cm}$

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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$\dfrac{p}{2}=125.6\ \ ,\ \ p=251.2$

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$\dfrac{p}{2}$	$=125.6$
$p$	$=2\times 125.6$
$p$	$=251.2$

$\therefore\ \text{The number is }251.2$

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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$3w=141\ \ ,\ \ w=47$

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$3w$	$=141$
$w$	$=\dfrac{141}{3}$
$w$	$=47$

$\therefore\ \text{The number is }47$

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)

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

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$\dfrac{x}{4}$	$=124\ 500$
$x$	$=4\times 124\ 500$
$x$	$=498\ 000$

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

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$x+15$	$=42$
$x$	$=42-15$
$x$	$=27$

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

\(c^2\)	\(=a^2+b^2\)
\(c^2\)	\(=12^2+14^2\)
\(c^2\)	\(=144+196\)
\(\sqrt{c^2}\)	\(=\sqrt{340}\)
\(c\)	\(=18.4390\ldots\)
	\(\approx 18.44\)

\(c^2\)	\(=a^2+b^2\)
\(c^2\)	\(=7^2+24^2\)
\(c^2\)	\(=49+576\)
\(\sqrt{c^2}\)	\(=\sqrt{625}\)
\(c\)	\(=25\)

\(A\)	\(=\pi r^2\)
\(\pi r^2\)	\(=10\)
\(r^2\)	\(=\dfrac{10}{\pi}\)
\(\sqrt{r^2}\)	\(=\sqrt{\dfrac{10}{\pi}}\)
\(r\)	\(=1.784\ldots\)
	\(\approx 1.8\ (1\text{ d.p.})\)

\(x^2+3\)	\(=147\)
\(x^2\)	\(=147-3\)
\(x^2\)	\(=144\)
\(\sqrt{x^2}\)	\(=\sqrt{144}\)
\(x\)	\(=\pm12\)

\(x^2-1\)	\(=48\)
\(x^2\)	\(=48+1\)
\(x^2\)	\(=49\)
\(\sqrt{x^2}\)	\(=\sqrt{49}\)
\(x\)	\(=\pm7\)

a.	\(A\)	\(=s^2\)
	\(A\)	\(=121\ \ \text{(given)}\)
	\(\therefore\ s^2\)	\(=121\)
	\(\sqrt{s^2}\)	\(=\sqrt{121}\)
	\(s\)	\(=11\)

b.	\(\text{Perimeter}\)	\(=4\times s\)
		\(=4\times 11\)
		\(=44\)

a.	\(A\)	\(=s^2\)
	\(A\)	\(=36\ \ \text{(given)}\)
	\(\therefore\ s^2\)	\(=36\)
	\(\sqrt{s^2}\)	\(=\sqrt{36}\)
	\(s\)	\(=6\)

b.	\(\text{Perimeter}\)	\(=4\times s\)
		\(=4\times 6\)
		\(=24\)