the quotient is
Question:

When $15 \sqrt{15}$ is divided by $3 \sqrt{3}$, the quotient is

(a) $5 \sqrt{3}$

(b) $3 \sqrt{5}$

(c) $5 \sqrt{5}$

(d) $3 \sqrt{3}$

Solution:

$15 \sqrt{15} \div 3 \sqrt{3}$

$=\frac{15 \sqrt{5 \times 3}}{3 \sqrt{3}}$

$=\frac{15 \times \sqrt{5} \times \sqrt{3}}{3 \sqrt{3}} \quad[\sqrt{a b}=\sqrt{a} \times \sqrt{b}]$

$=5 \sqrt{5}$

Hence, the correct answer is option (c).