Question

Find the least number with which 7938 should be divided to make it a perfect square? ​

Answer 1

$Resolving \: 7938 \: into \: prime \:factors , we \\get$

2 | 7938

_________

3 | 3969

_________

3 | 1323

_________

3 | 441

_________

3 | 147

_________

7 | 49

_________

**** 7

7938 = 2 × 3 × 3 × 3 × 3 × 7 × 7

The prime factor 2 doesn't appear in a group of two factors .

So, 7938 is not a perfect square.

Hence, the smallest number which is to be divided to make it a perfect square is 2.

$\red { Required \: perfect \: square } \\= \frac{7938}{2} \\= 3969$

= 3 × 3 × 3 × 3 × 7 × 7

= ( 3 × 3 × 7 )²

= 42² ( Perfect square )

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