Question

768 - By which smallest number this number should be multiplied, so that the result becomes a perfect square? Find the square root of the result obtained.

Answer 1

Hey Mate !!

The prime Factorization of 768 is,

768 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 3

Here, We can see the number 2 is paired 4 times while 3 is remained unpaired.

When we multiply 768 with 3. The product is 768 × 3 = 2304

The prime Factorization of 2304 is

2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

All numbers are paired. Hence, 2304 is a perfect square. The Square root is :

= 2 × 2 × 2 × 2 × 3

= 48

Therefore,

The Square root of 2304 is 48

Answer 2

Solution :

Resolving 768 into prime factors,

we get

768 = 2×2×2×2×2×2×2×2×3

=(2×2)(2×2)(2×2)(2×2)×3

We can see that 2,2,2 and 2

exists in pairs.

3 is alone .

So,we should multiply the

given number by 3 to get a

perfect square .

Therefore,

the perfect square obtained is

768 × 3 = 2304 = ( 48 )²

Square root = √2304 = 48

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