Question

In the following exercises, simplify.

$\sqrt{\frac{180s^{10}}{144}}$

Short answer

The required answer is$\frac{\sqrt{5}{s}^5}{2}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\sqrt{\frac{180s^{10}}{144}}$

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

$\sqrt{\frac{180s^{10}}{144}}$

Simplify the fraction inside the radical first. Rewrite showing common factors,

$\sqrt{\frac{12·3·5s^{10}}{12·3·4}}$

Simplify the fraction by removing common factors,

$\sqrt{\frac{5s^{10}}{4}}$

Rewrite using the quotient property,

role="math" localid="1648288020590" $\frac{\sqrt{5s^{10}}}{\sqrt{4}}$

Simplify,

$\frac{\sqrt{5}{s}^5}{2}$