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

Indices, SM-Bank 046

Write \(324\) as a product of its prime factors in index form.  (2 marks)

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\(2^2\times3^4\)

Show Worked Solution
\(324\) \(=4\times 81\)
  \(=2\times 2\times 9\times 9\)
  \(=2\times 2\times 3\times 3\times 3\times 3\)
  \(=2^2\times3^4\)