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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 1152 must be divided so that it becomes a perfect square. Also, find the square root of the number so obtained.
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Answer

The prime factorisation of 1152,
1152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
Grouping the factors into pairs of equal factors, we get,
1152 = (2 × 2) × (2 × 2) × (2 × 2) × (3 × 3) × 2
The factor, 2, at the end, does not have a pair. Therefore, we must divide 1152 by 2 to make a perfect square. The new number is,
(2 × 2) × (2 × 2) × (2 × 2) × (3 × 3) = 576
Taking one factor from each pair on the LHS, the square root of the new number is 2 × 2 × 2 × 3, which is equal to 24

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