Question

In the following exercises, simplify.

$\sqrt{\frac{45r^3}{s^{10}}}$

Short answer

The required answer is$\frac{3r\sqrt{5r}}{s^5}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\sqrt{\frac{45r^3}{s^{10}}}$

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

$\sqrt{\frac{45r^3}{s^{10}}}$

Rewrite using the quotient property,

$\frac{\sqrt{45r^3}}{\sqrt{s^{10}}}$

Simplify the radicals in the numerator and the denominator,

$\frac{\sqrt{9r^2}·\sqrt{5r}}{\sqrt{s^{10}}}$

Simplify,

$\frac{3r\sqrt{5r}}{s^5}$