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Squares and Square Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSSquares and Square Roots2 Marks
Question
Using prime factorization method, find the following numbers are perfect squares? $11025$
✓

Answer

$11025 = 3 \times 3 \times 5 \times 5 \times 7 \times 7$
$\begin{array}{c|c} 3& 11025 \\ \hline 3 & 3675 \\\hline 5&1225 \\\hline 5&245 \\\hline 7&49 \\\hline 7&7 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
$11025 = (3 \times 2) \times (5 \times 5) \times (7 \times 7)$
There are no left out of pairs.
Hence, $11025$ is a perfect square.

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