Question

By what number should 216 be divided so that the quotient is a perfect square

Answer 1

Prime factors of 216 = 2×2×2×3×3×3

Grouping the factors into pairs of equal factors with 2 and 3

216 = 2×2×2×3×3×3

We find there is no prime factors to form a pair with 2 and 3

Therefore, we must divide the number by 6,so that number becomes a perfect square.

If we divide the given number by 2×3 = 6,then

New number = 216÷6 = 36

Taking one factors from each, we get square root of new number(quotient)
= 2×3 = 6