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Indices, SM-Bank 059

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

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

Show Answers Only

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