Q. 8.98 - Intermediate Algebra

Question

Simplify:

$\frac{\sqrt{96a^5{b}^4}}{\sqrt{2a^{3}b}}$

Step-by-Step Solution

Answer

The simplification of $\frac{\sqrt{96a^5{b}^4}}{\sqrt{2a^{3}b}}$ is $4ab\sqrt{3b}$

Step 1. Given

An expression $\frac{\sqrt{96a^5{b}^4}}{\sqrt{2a^{3}b}}$

To simplify the expression 

Step 2. Rewrite using the quotient property

Rewrite using the quotient property 

$\frac{\sqrt{96a^5{b}^4}}{\sqrt{2a^{3}b}}=\sqrt{\frac{96a^5{b}^4}{2a^{3}b}}$

Remove the common factors. 

                 $=\sqrt{48a^2{b}^3}$

Step 3. Rewrite the radical as the product of two radicals.

$\frac{\sqrt{96a^5{b}^4}}{\sqrt{2a^{3}b}}=\sqrt{48a^2{b}^3}$

                  $=\sqrt{16a^2{b}^2}.\sqrt{3b}$

                  $=4ab\sqrt{3b}$

The simplification of the expression is $4ab\sqrt{3b}$