Simplify the Radical Expression (4 square root of 2)/(3 square root of 8)

$\frac{4 \sqrt{2}}{3 \sqrt{8}}$

Step 1

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

$\frac{4 \sqrt{\frac{2}{8}}}{3}$

Step 2

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

Factor $2$ out of $2$ .

$\frac{4 \sqrt{\frac{2 (1)}{8}}}{3}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{4 \sqrt{\frac{2 \cdot 1}{2 \cdot 4}}}{3}$

Cancel the common factor.

$\frac{4 \sqrt{\frac{2 \cdot 1}{2 \cdot 4}}}{3}$

Rewrite the expression.

$\frac{4 \sqrt{\frac{1}{4}}}{3}$

Step 3

Simplify the numerator.

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

$\frac{4 \frac{\sqrt{1}}{\sqrt{4}}}{3}$

Any root of $1$ is $1$ .

$\frac{4 \frac{1}{\sqrt{4}}}{3}$

Simplify the denominator.

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

$\frac{4 \frac{1}{\sqrt{2^{2}}}}{3}$

Pull terms out from under the radical.

$\frac{4 \frac{1}{| 2 |}}{3}$

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

$\frac{4 (\frac{1}{2})}{3}$

Step 4

Combine $4$ and $\frac{1}{2}$ .

$\frac{\frac{4}{2}}{3}$

Step 5

Divide $4$ by $2$ .

$\frac{2}{3}$