Question

by what number should 5292 be divided so as to make it a perfect square. also find the square root of number so formed.​

Answer 1

$Resolving \:5292 \:into \:prime \:factors , \:we$

$get$

2| 5292

________

2| 2646

________

3| 1323

________

3| 441

________

3| 147

________

7| 49

________

**** 7

5292 = 2×2 × 3× 3×3 × 7×7

We can see that , 2, 3 and 7 exists in pairs while 3 is alone .

So, we must divide the given number by 3.

$i)\red{Required \: perfect \:square}$

$= \frac{ 5292}{3}$

$= 1764$

$= ( 42 )^{2} \: ( Perfect \: square )$

$ii)\red{ Square \:root \: of \: 1764 }$

$= \sqrt{ 42^{2}}$

$= 42$

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