Question

In the following exercises, simplify.

$\sqrt{\frac{25r^8}{64r}}$

Short answer

The required answer is $\frac{5r^3\sqrt{r}}{8}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\sqrt{\frac{25r^8}{64r}}$

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

$\sqrt{\frac{25r^8}{64r}}$

Simplify the fraction inside the radical first.

$\sqrt{\frac{25r^7}{64}}$

Rewrite using the quotient property,

$\frac{\sqrt{25r^7}}{\sqrt{64}}$

Simplify the radicals in the numerator and the denominator,

$\frac{\sqrt{25r^6}·\sqrt{r}}{\sqrt{64}}$

Simplify,

$\frac{5r^3\sqrt{r}}{8}$