Question

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

Answer 1

1100 = 11* 100 = 11* 10 * 10
It can be found that 10*10 is a perfect square.
So to make the remaining part a perfect square, just multiply it by '11'
1100 * 11 = 11*11*10*10
Now this is a perfect square.Square root (1100*11) = 11*10 = 110 
Hence the smallest number to be multiplied to make it a perfect square is '11' and the square root of that perfect square number is '110'
Hope it helps.