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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.

A
8,48
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B
7,42
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C
9,42
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D
7,48
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Solution

## The correct option is B 7,42252=2×2––––––×3×3––––––×7The prime factor 7 does not appear in pairs. To make 252 a perfect square we need one more 7.Hence, the smallest number by which 252 must be multiplied so thatthe product is a perfect square is 7.And, 252×7=2×2––––––×3×3––––––×7×7––––––√252×7=√2×2––––––×3×3––––––×7×7––––––=2×3×7=42

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