Basic Math Examples

\sqrt{\frac{32}{25}}

$\sqrt{\frac{32}{25}}$

Step 1

Rewrite

\sqrt{\frac{32}{25}}

$\sqrt{\frac{32}{25}}$ as

\frac{\sqrt{32}}{\sqrt{25}}

$\frac{\sqrt{32}}{\sqrt{25}}$ .

\frac{\sqrt{32}}{\sqrt{25}}

$\frac{\sqrt{32}}{\sqrt{25}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

32

$32$ as

4^{2} \cdot 2

$4^{2} \cdot 2$ .

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Step 2.1.1

Factor

16

$16$ out of

32

$32$ .

\frac{\sqrt{16 (2)}}{\sqrt{25}}

$\frac{\sqrt{16 (2)}}{\sqrt{25}}$

Step 2.1.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

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

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

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

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

Step 2.2

Pull terms out from under the radical.

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

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

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

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

Step 3

Simplify the denominator.

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Step 3.1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

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

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

Step 3.2

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

\frac{4 \sqrt{2}}{5}

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

\frac{4 \sqrt{2}}{5}

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

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{4 \sqrt{2}}{5}

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

Decimal Form:

1.13137084 \dots

$1.13137084 \dots$