Question

In the following exercises, simplify.

$\sqrt{\frac{72x^5}{y^6}}$

Short answer

The required answer is$\frac{6x^2\sqrt{2x}}{y^3}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\sqrt{\frac{72x^5}{y^6}}$

Step 2. Use the quotient property to simplify the square root.

$\sqrt{\frac{72x^5}{y^6}}$

Rewrite using the quotient property,

$\frac{\sqrt{72x^5}}{\sqrt{y^6}}$

Simplify the radicals in the numerator and the denominator,

role="math" localid="1648291082776" $\frac{\sqrt{36x^4}·\sqrt{2x}}{\sqrt{y^6}}$

Simplify,

$\frac{6x^2\sqrt{2x}}{y^3}$