Basic Math Examples

$\frac{\sqrt{\sqrt{50}} \cdot 12}{\sqrt{5}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.1.1

Factor $25$ out of $50$ .

$\frac{\sqrt{\sqrt{25 (2)}} \cdot 12}{\sqrt{5}}$

Step 1.1.2

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{\sqrt{5^{2} \cdot 2}} \cdot 12}{\sqrt{5}}$

Step 1.2

Pull terms out from under the radical.

$\frac{\sqrt{5 \sqrt{2}} \cdot 12}{\sqrt{5}}$

Step 2

Move $12$ to the left of $\sqrt{5 \sqrt{2}}$ .

$\frac{12 \sqrt{5 \sqrt{2}}}{\sqrt{5}}$

Step 3

Combine $\sqrt{5 \sqrt{2}}$ and $\sqrt{5}$ into a single radical.

$12 \sqrt{\frac{5 \sqrt{2}}{5}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{5 \sqrt{2}}{5}$ by cancelling the common factors.

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Step 4.1.1

Cancel the common factor.

$12 \sqrt{\frac{5 \sqrt{2}}{5}}$

Step 4.1.2

Rewrite the expression.

$12 \sqrt{\frac{\sqrt{2}}{1}}$

Step 4.2

Divide $\sqrt{2}$ by $1$ .

$12 \sqrt{\sqrt{2}}$

Step 5

Rewrite $\sqrt{\sqrt{2}}$ as $\sqrt[4]{2}$ .

$12 \sqrt[4]{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt[4]{2}$

Decimal Form:

$14.27048538 \dots$