Question

In the following exercises, simplify.

$\sqrt{\frac{49r^{12}}{16r^6}}$

Short answer

The required answer is$\frac{7r^3}{4}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\sqrt{\frac{49r^{12}}{16r^6}}$

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

$\sqrt{\frac{49r^{12}}{16r^6}}$

Simplify the fraction inside the radical first.

$\sqrt{\frac{49r^6}{16}}$

Rewrite using the quotient property,

$\frac{\sqrt{49r^6}}{\sqrt{16}}$

Simplify,

$\frac{7r^3}{4}$