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Squares and Square Roots — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsSquares and Square Roots3 Marks
Question
Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.
✓

Answer

By prime factorisation, we get
252 = 2 × 2 × 3 × 3 × 7
So, the given number should be multiplied by 7 to make the product a perfect square.
New number = 252 × 7 = 1764
$\therefore$ 1764 = 2 × 2 × 3 × 3 × 7 × 7
$\sqrt{1764}=2\times3\times7=42$

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