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