Algebra Examples

$\sqrt{2}$ , $\sqrt{8}$

Step 1

Divide the first expression by the second expression.

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

Step 2

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

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

Step 3

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

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Step 3.1

Factor $2$ out of $2$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $8$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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

Step 5

Any root of $1$ is $1$ .

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

Step 6

Simplify the denominator.

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Step 6.1

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

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

Step 6.2

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

$\frac{1}{2}$