Question

Is 112 a perfect square? If ‘no’ find out the smallest number that can be multiplied to make it a perfect square.

Answer 1

Hey Mate !!

No, 112 is not a perfect square.

Reason :

The prime Factorization of 112 is,

112 = 2 × 2 × 2 × 2 × 7

Here, 2 is paired 2 times while 7 is remained unpaired. Hence 112 is not a perfect square. To make it a perfect square we should multiply the number with 7. When we multiply 112 with 7 the product is 784.

The prime Factorization of 784 is

784 = 2 × 2 × 2 × 2 × 7 × 7

= 2 × 2× 7

= 28

The Square root is 28.

Answer 2

Given 112

Resolve 112 into product of

prime factors , we get

112 = 2×2×2×2×7

= ( 2×2)×(2×2)×7

Here , 2 is paired ,

But 7 is alone .

Therefore ,

112 is not a perfect square .

Smallest number multiplied to

make it perfect square is 7.

Now ,

112 × 7 = 2² × 2² × 7²

= ( 2×2×7 )²

= 28² [ perfect square ]

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