Question

find the smallest number by which 1100 must be multiplied so that the product becomes a prefect square . find the squres root of the prefect squre so obtainted

Answer 1

Prime factorization of 1100:

1100 = 2 x 550

        = 2 x 2 x 275

        = 2 x 2 x 5 x 55

        = 2 x 2 x 5 x 5 x 11

It can be written as 1100 = 2² x 5² x 11

In order to make it a perfect square, 1100 should be multiplied by 11

1100x11 = 2² x 5² x 11 x 11 = 2² x 5² x 11² = 12100.

So the perfect square obtained by multiplying 1100 by 11 is 12100.

The square root of obtained perfect square = √12100 = 110