Q. 255 - Intermediate Algebra

Question

In the following exercises, simplify. 

$\frac{\sqrt{56x^5{y}^4}}{\sqrt{2x{y}^3}}$

Step-by-Step Solution

Answer

The simplified form is $2x^2\sqrt{7y}$.

Step 1. Given information.

The given expression is 

$\frac{\sqrt{56x^5{y}^4}}{\sqrt{2x{y}^3}}$.

Step 2. Simplifying.

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

$\frac{\sqrt{56x^5{y}^4}}{\sqrt{2x{y}^3}}=\sqrt{\frac{56x^5{y}^4}{2x{y}^3}}$

Then removing the common factors.

$\sqrt{\frac{56x^5{y}^4}{2x{y}^3}}=\sqrt{28x^{4}y}$

On simplifying we get,

$\sqrt{28x^{4}y}=2x^2\sqrt{7y}$

Hence, the simplified form is $2x^2\sqrt{7y}$.