Simplify the Radical Expression ( square root of 125)÷( square root of 5)

$\sqrt{125} \div \sqrt{5}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{125}}{\sqrt{5}}$

Step 2

Combine $\sqrt{125}$ and $\sqrt{5}$ into a single radical.

$\sqrt{\frac{125}{5}}$

Step 3

Divide $125$ by $5$ .

$\sqrt{25}$

Step 4

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

Step 5

Pull terms out from under the radical.

$| 5 |$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$5$