SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Indices, SM-Bank 061

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

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

Show Answers Only

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