Gujarat BoardEnglish MediumSTD 8MATHSSquares and Square Roots3 Marks
Question
Find the square root of the following by prime factorization.$47089$
✓
Answer
Resolving $47089$ into prime factors, $47089 = 7 \times 7 \times 31 \times 31$
$\begin{array}{c|c}7& 47089 \\ \hline 7 & 6727 \\\hline 31&961 \\\hline31&31 \\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $47089 = (7 \times 7) \times (31 \times 31)$
Taking one factor for each pair, we get the square root of $47089 7 \times 31 = 217$
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