To find the smallest number by which -147 should be multiplied to get a perfect square, we need to find the prime factorization of -147.

The prime factorization of -147 is -1 * 3 * 7 * 7.

To make it a perfect square, we need to multiply it by the missing prime factors. In this case, the missing prime factor is 3.

So, -147 should be multiplied by 3 to get a perfect square: -147 * 3 = -441.

The square root of -441 is 21.

Therefore, the smallest number by which -147 should be multiplied to get a perfect square is 3, and the square root of the square number obtained (-441) is 21.