Q. 256 - Intermediate Algebra

Question

In the following exercises, simplify. 

$\frac{\sqrt{72a^3{b}^6}}{\sqrt{3a{b}^3}}$

Step-by-Step Solution

Answer

The simplified form is $2ab\sqrt{6b}$.

Step 1. Given information.

The given expression is

$\frac{\sqrt{72a^3{b}^6}}{\sqrt{3a{b}^3}}$. 

Step 2. Simplifying.

Now, to simplify the expression first we will rewrite the expression using the quotient property.

$\frac{\sqrt{72a^3{b}^6}}{\sqrt{3a{b}^3}}=\sqrt{\frac{72a^3{b}^6}{3a{b}^3}}$

Then removing the common factors. 

$\sqrt{\frac{72a^3{b}^6}{3a{b}^3}}=\sqrt{24a^2{b}^3}$

On simplifying we get, 

$\sqrt{24a^2{b}^3}=2ab\sqrt{6b}$

Hence, the simplified form is $2ab\sqrt{6b}$.