Question

find the smallest number by which 1100 must be multiplied so that product becomes a perfect square . Also find the square root of perfect square so obtained .​

Answer 1

For doing this, you have to factories 1100.

1100 = 2 * 550

550 = 2 * 275

275 = 5 * 55

55 = 5 * 11

So, 1100 = 2 * 2 * 5 * 5 * 11, so only 11 is found odd times in this factorization, so we need to multiply it by 11.

So, on multiplication it will be 12100 and root of it is, 2 * 5 * 11, which is 110.

Answer : 110