Question

find square root of 1024 by prime factorization method

Answer 1

$1024 \div 2 = 512 \\ 512 \div 2 = 256 \\ 256 \div 2 = 128 \\ 128 \div 2 = 64 \\ 64 \div 2 = 32 \\ 32 \div 2 = 16 \\ 16 \div 2 = 8 \\ 8 \div 2 = 4 \\ 4 \div 2 = 2 \\ 2 \div 2 = 1 \\ 1024 = {2}^{10} \\ \sqrt{1024} = \sqrt{ {2}^{10} } \\ = {2}^{5} \\ = 32$

Answer 2

✪ SOLUTION ✪

✪ We have to factorise 1024

✪ Let us factorise

$\begin{array}{r | 1} 2 & 1024 \\ \cline{2-2} 2 & 512 \\ \cline{2-2} 2 & 256 \\ \cline{2-2} 2 & 128 \\ \cline{2-2} 2 & 64 \\ \cline{2-2} 2 & 32 \\ \cline{2-2} 2 & 16 \\ \cline{2-2} 2 & 8 \\ \cline{2-2} 2 & 4 \\ \cline{2-2} 2 & 2 \\ \cline{2-2} & 1\end{array}$

∴ 1024 = 2×2 × 2×2 × 2×2 × 2×2 × 2×2

✪ Now we have to take one factor of

   each pair

√1024 = 2 × 2 × 2 × 2 × 2

           = 32