Finite Math Examples

$\sqrt{\frac{1}{2}} \sqrt{\frac{1}{32}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{1}{2} \cdot \frac{1}{32}}$

Step 2

Multiply $\frac{1}{2}$ by $\frac{1}{32}$ .

$\sqrt{\frac{1}{2 \cdot 32}}$

Step 3

Multiply $2$ by $32$ .

$\sqrt{\frac{1}{64}}$

Step 4

Rewrite $\sqrt{\frac{1}{64}}$ as $\frac{\sqrt{1}}{\sqrt{64}}$ .

$\frac{\sqrt{1}}{\sqrt{64}}$

Step 5

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{64}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $64$ as $8^{2}$ .

$\frac{1}{\sqrt{8^{2}}}$

Step 6.2

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

$\frac{1}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$