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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.24336
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Answer

Resolving 24336 into prime factors,
24336 = 2 × 2 × 2 × 2 × 3 × 3 × 13 × 13
$\begin{array}{c|c}2& 24336 \\ \hline 2 & 12168 \\\hline 2&6084 \\\hline2&3042 \\\hline3&1521 \\\hline 3&507\\\hline13&169\\\hline13&13\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
24336 = (2 × 2) × (2 × 2) × (3 × 3) × (13 × 13)
Taking one factor for each pair, we get the square root of 24336
2 × 2 × 3 × 13 = 156

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