A number is a perfect square if it is equal to an integer raised to the square. For example, $25=5^{2}, 49=7^{2}$ and $125=25^{2}$ are perfect squares. What is the smallest number by which we must multiply 120 to obtain a perfect square?
(a) 10
(b) 15
(c) 20
(d) 30
(e) 35
The correct option is (d).

Factoring 120 we get $120=2^{3} \times 3 \times 5$. To obtain a perfect square, all the exponents in this factorization must be even, so it is enough to multiply 120 by

$$
2 \times 3 \times 5=30
$$

Indeed, we have, $120 \times 30=2^{3} \times 3 \times 5 \times 2 \times 3 \times 5=2^{4} \times 3^{2} \times 5^{2}=\left(2^{2} \times 3 \times 5\right)^{2}=60^{2}$.