Question

what is the smallest number by which 73500 should be divided to obtain a perfect square

Answer 1

We have to determine the smallest number by which 73500 should be divided to obtain a perfect square.

Firstly, we will find the factors of 73500.

73500 = $2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 7 \times 7$

73500 = $2^ 2 \times 3 \times 5^3 \times 7^2$

73500 = $2^ 2 \times 3 \times 5^2 \times 5 \times 7^2$

73500 = $2^ 2 \times 5^2 \times 7^2 \times 15$

Here, we can observe the numbers 2, 5 and 7 have powers of 2.

15 does'not have power of 2.

Therefore, 73500 should be divided by 15 to form a perfect square.