Basic Math Examples

$\sqrt{\frac{5}{2}} \cdot \sqrt{\frac{125}{8}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{5}{2} \cdot \frac{125}{8}}$

Step 2

Multiply $\frac{5}{2}$ by $\frac{125}{8}$ .

$\sqrt{\frac{5 \cdot 125}{2 \cdot 8}}$

Step 3

Multiply.

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Step 3.1

Multiply $5$ by $125$ .

$\sqrt{\frac{625}{2 \cdot 8}}$

Step 3.2

Multiply $2$ by $8$ .

$\sqrt{\frac{625}{16}}$

Step 4

Rewrite $\sqrt{\frac{625}{16}}$ as $\frac{\sqrt{625}}{\sqrt{16}}$ .

$\frac{\sqrt{625}}{\sqrt{16}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $625$ as $25^{2}$ .

$\frac{\sqrt{25^{2}}}{\sqrt{16}}$

Step 5.2

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

$\frac{25}{\sqrt{16}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $16$ as $4^{2}$ .

$\frac{25}{\sqrt{4^{2}}}$

Step 6.2

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

$\frac{25}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{4}$

Decimal Form:

$6.25$

Mixed Number Form:

$6 \frac{1}{4}$