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Squares and Square Roots — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsSquares and Square Roots2 Marks
Question
Using prime factorization method, find the following numbers are perfect squares?
3549
✓

Answer

3549 = 3 × 7 × 13 × 13
$\begin{array}{c|c} 3& 3549 \\ \hline 7 & 1183 \\\hline 13&169 \\\hline 13&13 \\\hline &1 \end{array}$
Grouping them into pairs of equal factors,
3549 = (13 × 13) × 3 × 7
The last factors, 3 and 7 cannot be paired. Hence, 3549 is not a perfect square.
Hence, the perfect squares are 225, 441, 2916 and 11025.

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