Find the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number.

We need to find the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number.

Let the smallest number be 𝑥.

According to the given statement,  $\sqrt{1200\times x}$   must be a rational number. Now, it can also be written as

⇒$\sqrt{2\times 2\times 2\times 2\times 3\times 5\times 5\times x}$

⇒ 20$\sqrt{3\times x}$

Now, if we take as 3, then the result would be a rational number. Hence, the smallest number is 3.