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Squares and Square Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSSquares and Square Roots2 Marks
Question
Using the prime factorisation method, find the following numbers are perfect squares:
$5625$
✓

Answer

A perfect square can always be expressed as a product of equal factors.
Resolving into prime factors:
$5625$
$= 225 × 25$
$= 9 × 25 × 25$
$= 3 × 3 × 5 × 5 × 5 × 5$
$= 3 × 5 × 5 × 3 × 5 × 5$
$= 75 × 75$
$= (75)^2$
Thus, $5625$ is a perfect square.

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