Question:
By what smallest number should 216 be divided, so that the quotient
is’ a perfect square? Also, find the square root of the quotient.
Solution:
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)
$=2 \times 3=6$