Question

Find the smallest number by which $300$ must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Answer 1

$300=2\times 2\times 5\times 5\times 3$

We observe that $2$ and $5$ are grouped in pairs and the $3$ is left unpaired.

If we multiply $300$ by the factoe $3$ then

$300\times 3=2\times 2\times 5\times 5\times 3\times 3$

$900=2\times 2\times 5\times 5\times 3\times 3$ which is a perfect square.

$\therefore$ Required number is $3$

$\sqrt{900}=30$