By what smallest number should 216 be divided,

Prime factors of $216=2 \times 2 \times 2 \times 3 \times 3 \times 3$

Grouping the factors into pairs of equal factors, we get

$216=2 \times 2 \times 2 \times 3 \times 3 \times 3$

We find that there is no prime factor to form a pair with 2 and $3 .$

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

If we divide the given number by $2 \times 3$ i.e. 6 , then

New number $=\frac{216}{6}=36$

Taking one factor from each, we get square root of new number (quotient)

$=2 \times 3=6$