Simplify the Radical Expression ( square root of 2)/(4 square root of 8)

$\frac{\sqrt{2}}{4 \sqrt{8}}$

Step 1

Combine $\sqrt{2}$ and $\sqrt{8}$ into a single radical.

$\frac{\sqrt{\frac{2}{8}}}{4}$

Step 2

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2$ .

$\frac{\sqrt{\frac{2 (1)}{8}}}{4}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{\sqrt{\frac{2 \cdot 1}{2 \cdot 4}}}{4}$

Cancel the common factor.

$\frac{\sqrt{\frac{2 \cdot 1}{2 \cdot 4}}}{4}$

Rewrite the expression.

$\frac{\sqrt{\frac{1}{4}}}{4}$

Step 3

Simplify the numerator.

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$\frac{\frac{\sqrt{1}}{\sqrt{4}}}{4}$

Any root of $1$ is $1$ .

$\frac{\frac{1}{\sqrt{4}}}{4}$

Simplify the denominator.

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

$\frac{\frac{1}{\sqrt{2^{2}}}}{4}$

Pull terms out from under the radical.

$\frac{\frac{1}{| 2 |}}{4}$

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

$\frac{\frac{1}{2}}{4}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{1}{4}$

Step 5

Multiply $\frac{1}{2} \cdot \frac{1}{4}$ .

Multiply $\frac{1}{2}$ by $\frac{1}{4}$ .

$\frac{1}{2 \cdot 4}$

Multiply $2$ by $4$ .

$\frac{1}{8}$