Simplify (8 square root of 2)/(2 square root of 8)

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

Step 1

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

Factor $2$ out of $8 \sqrt{2}$ .

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

Cancel the common factors.

Factor $2$ out of $2 \sqrt{8}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

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

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

Step 5

Any root of $1$ is $1$ .

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

Step 6

Simplify the denominator.

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

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

Pull terms out from under the radical, assuming positive real numbers.

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

Step 7

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2$

Simplify (8 square root of 2)/(2 square root of 8)

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