Simplify the Radical Expression ( square root of 9)/( square root of 25)

$\frac{\sqrt{9}}{\sqrt{25}}$

Step 1

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2}}}{\sqrt{25}}$

Pull terms out from under the radical.

$\frac{| 3 |}{\sqrt{25}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{3}{\sqrt{25}}$

Step 2

Simplify the denominator.

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

$\frac{3}{\sqrt{5^{2}}}$

Pull terms out from under the radical.

$\frac{3}{| 5 |}$

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

$\frac{3}{5}$