Simplify the Radical Expression square root of 8/25

$\sqrt{\frac{8}{25}}$

Step 1

Rewrite $\sqrt{\frac{8}{25}}$ as $\frac{\sqrt{8}}{\sqrt{25}}$ .

$\frac{\sqrt{8}}{\sqrt{25}}$

Step 2

Simplify the numerator.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2)}}{\sqrt{25}}$

Rewrite $4$ as $2^{2}$ .

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

Pull terms out from under the radical.

$\frac{| 2 | \sqrt{2}}{\sqrt{25}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 3

Simplify the denominator.

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

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

Pull terms out from under the radical.

$\frac{2 \sqrt{2}}{| 5 |}$

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.56568542 \dots$