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

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