Question

find the smallest number by which 600 must be divided so that quotient becames a perfect square also find the square root of the perfect square so obtained

Answer 1

The smallest no. which must be divided by 600 to get the quotient a perfect square.

So, First we will do Factorisation
600=2×2×2×3×5×5
Now, we will make pairs of two and the left nos. will be divided...
600=2×5
$\frac{600}{3 \times 2}$
$\frac{600}{6} =100$
$\sqrt{100} = {10}^{2}$