Question

find the smallest number by which 1008 must be multiplied to get a perfect square. also find the square root of the perfect square so obtained​

Answer 1

We know that

It can be written as

1008 = 2×2×2×2×3×3×7

Here

After pairing the same prime factors, one factor 7 is left.

Now multiplying 1008 by 7

We get perfect square

Therefore, the required smallest number is 7.