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. $15\sqrt{3}$

Answer 1

The correct option is C $5\sqrt{5}$

$\Rightarrow$ $15\sqrt{15}=(15{)}^1\times (15{)}^{\frac{1}{2}}=(15{)}^{1+\frac{1}{2}}=(15{)}^{\frac{3}{2}}$

$\Rightarrow$ $3\sqrt{3}=(3{)}^1\times (3{)}^{\frac{1}{2}}=(3{)}^{\frac{3}{2}}$

$\Rightarrow$ Now, $15\sqrt{15}÷3\sqrt{3}$

$=$ $(15{)}^{\frac{3}{2}}÷(3{)}^{\frac{3}{2}}$

$=$ $\frac{(15{)}^{\frac{3}{2}}}{(3{)}^{\frac{3}{2}}}$

$=$ ${\left(\frac{15}{3}\right)}^{\frac{3}{2}}$

$=$ $(5{)}^{\frac{3}{2}}$

$=$ $\sqrt{125}=5\sqrt{5}$

$\therefore$ The required quetient is $5\sqrt{5}$.