Question

find the smallest number by which 23814 must be divided so that it becomes a perfect square. Find the square root of the perfect square so obtained​

Answer 1

the square root of the perfect square so obtained is 6

Answer 2

$Resolving \: 23814 \:into \: prime \:factors, we \\get$

2 | 23814

________

3 | 11907

________

3 | 3969

________

3 | 1323

________

3 | 441

________

3 | 147

________

7 | 49

________

**** 7

23814 = 2 × 3 × 3 × 3 × 3 × 3 × 7 × 7

we can see that , 3, 3 and 7 exists in pairs while 2 and 3 do not exists in pair.

So, we must divide the given number by 2 × 3 = 6

$\therefore perfect \: square \: obtained \\= 23814 \div 6\\= 3969$

$\red{ The \: square \:root \:of \: 3969}\\= \sqrt{ 3 \times 3 \times 3 \times 3 \:times 7 \times 7 }\\= 3 \times 3 \times 7 \\= \green { = 63 }$

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