Maharashtra BoardEnglish MediumSTD 8MathsSquares and Square Roots3 Marks
Question
Find the square root of the following by prime factorization.1156
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Answer
Resolving 1156 into prime factors,
1156 = 2 × 2 × 17 × 17
$\begin{array}{c|c}2& 1156 \\ \hline 2 & 578 \\\hline 17&289 \\\hline17&17 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors,
1156 = (2 × 2) × (17 × 17)
Taking one factor for each pair, we get the square root of 1764,
2 × 17 = 34
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