Question

find the smallest number by which 5292 must be multiplied to get a perfect square.also find tje square root of perfect square so obtained​

Answer 1

★ Solution ★

★According to the question,

   we have to factorise 5292

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Let us do it,

$\begin{array}{r | 1} 2 & 5292 \\ \cline{2-2} 2 & 2646 \\ \cline{2-2} 3 & 1323 \\ \cline{2-2} 3 & 441 \\ \cline{2-2} 3 & 147 \\ \cline{2-2} 7 & 49 \\ \cline{2-2} 7 & 7 \\ \cline{2-2} & 1\end{array}$

5292 = (2×2) × (3×3) × 3 × (7×7)

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★ We have seen from the above that 3

   has not any pair . So, we multiplied

   5292 by 3 to make it perfect square.

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Thus, the number which is obtain

on multiplying 5292 by 3

is 5292 × 3

= 2×2 × 3×3 × 3×3 × 7×7

= 15876

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15876 = (2×2) × (3×3) × (3×3) × (7×7)

          = 2² × 3² × 3² × 7²

          = 126²

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★ Therefore 5292 on multiplying 3

   become a perfect square of 126