Find the square root of the following by prime factorization.4096 - Vidyadip

Question

Find the square root of the following by prime factorization.4096

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Answer

Resolving 4096 into prime factors,
4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
$\begin{array}{c|c}2& 4096 \\ \hline 2 & 2048 \\\hline 2&1024 \\\hline2&512 \\\hline2&256\\\hline2&128\\\hline2&64\\\hline2&32\\\hline2&16\\\hline2&8\\\hline2&4\\\hline2&2\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
4096 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)
Taking one factor for each pair, we get the square root of 4096,
(2 × 2) × (2 × 2) × (2 × 2) = 64

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