Finite Math Examples

$\sqrt{\frac{7}{8} \cdot \sqrt{56}}$

Step 1

Combine $\frac{7}{8}$ and $\sqrt{56}$ .

$\sqrt{\frac{7 \sqrt{56}}{8}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $56$ as $2^{2} \cdot 14$ .

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Step 2.1.1

Factor $4$ out of $56$ .

$\sqrt{\frac{7 \sqrt{4 (14)}}{8}}$

Step 2.1.2

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

$\sqrt{\frac{7 \sqrt{2^{2} \cdot 14}}{8}}$

Step 2.2

Pull terms out from under the radical.

$\sqrt{\frac{7 \cdot 2 \sqrt{14}}{8}}$

Step 2.3

Multiply $7$ by $2$ .

$\sqrt{\frac{14 \sqrt{14}}{8}}$

Step 3

Cancel the common factor of $14$ and $8$ .

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Step 3.1

Factor $2$ out of $14 \sqrt{14}$ .

$\sqrt{\frac{2 (7 \sqrt{14})}{8}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $8$ .

$\sqrt{\frac{2 (7 \sqrt{14})}{2 (4)}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{2 (7 \sqrt{14})}{2 \cdot 4}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{7 \sqrt{14}}{4}}$

Step 4

Rewrite $\sqrt{\frac{7 \sqrt{14}}{4}}$ as $\frac{\sqrt{7 \sqrt{14}}}{\sqrt{4}}$ .

$\frac{\sqrt{7 \sqrt{14}}}{\sqrt{4}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{\sqrt{7 \sqrt{14}}}{\sqrt{2^{2}}}$

Step 5.2

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

$\frac{\sqrt{7 \sqrt{14}}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{7 \sqrt{14}}}{2}$

Decimal Form:

$2.55888655 \dots$