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Squares and Square Roots — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsSquares and Square Roots3 Marks
Question
Find the square root of the following by prime factorization.11664
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Answer

Resolving 11664 into prime factors,11664 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
$\begin{array}{c|c}2& 11644 \\ \hline 2 & 5832 \\\hline 2&2916 \\\hline2&1458 \\\hline3&729\\\hline3&243\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
11664 = (2 × 2) × (2 × 2) × (3 × 3) × (3 × 3) × (3 × 3)
Taking one factor for each pair, we get the square root of 11664
2 × 2 × 3 × 3 × 3 = 108

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