Basic Math Examples

$\sqrt{\frac{112}{25}}$

Step 1

Rewrite $\sqrt{\frac{112}{25}}$ as $\frac{\sqrt{112}}{\sqrt{25}}$ .

$\frac{\sqrt{112}}{\sqrt{25}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $112$ as $4^{2} \cdot 7$ .

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Step 2.1.1

Factor $16$ out of $112$ .

$\frac{\sqrt{16 (7)}}{\sqrt{25}}$

Step 2.1.2

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

$\frac{\sqrt{4^{2} \cdot 7}}{\sqrt{25}}$

Step 2.2

Pull terms out from under the radical.

$\frac{4 \sqrt{7}}{\sqrt{25}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{4 \sqrt{7}}{\sqrt{5^{2}}}$

Step 3.2

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

$\frac{4 \sqrt{7}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{7}}{5}$

Decimal Form:

$2.11660104 \dots$