Basic Math Examples

\sqrt{\frac{24}{25}}

$\sqrt{\frac{24}{25}}$

Step 1

Rewrite

\sqrt{\frac{24}{25}}

$\sqrt{\frac{24}{25}}$ as

\frac{\sqrt{24}}{\sqrt{25}}

$\frac{\sqrt{24}}{\sqrt{25}}$ .

\frac{\sqrt{24}}{\sqrt{25}}

$\frac{\sqrt{24}}{\sqrt{25}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

24

$24$ as

2^{2} \cdot 6

$2^{2} \cdot 6$ .

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Step 2.1.1

Factor

4

$4$ out of

24

$24$ .

\frac{\sqrt{4 (6)}}{\sqrt{25}}

$\frac{\sqrt{4 (6)}}{\sqrt{25}}$

Step 2.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\frac{\sqrt{2^{2} \cdot 6}}{\sqrt{25}}

$\frac{\sqrt{2^{2} \cdot 6}}{\sqrt{25}}$

\frac{\sqrt{2^{2} \cdot 6}}{\sqrt{25}}

$\frac{\sqrt{2^{2} \cdot 6}}{\sqrt{25}}$

Step 2.2

Pull terms out from under the radical.

\frac{2 \sqrt{6}}{\sqrt{25}}

$\frac{2 \sqrt{6}}{\sqrt{25}}$

\frac{2 \sqrt{6}}{\sqrt{25}}

$\frac{2 \sqrt{6}}{\sqrt{25}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\frac{2 \sqrt{6}}{\sqrt{5^{2}}}

$\frac{2 \sqrt{6}}{\sqrt{5^{2}}}$

Step 3.2

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

\frac{2 \sqrt{6}}{5}

$\frac{2 \sqrt{6}}{5}$

\frac{2 \sqrt{6}}{5}

$\frac{2 \sqrt{6}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{2 \sqrt{6}}{5}

$\frac{2 \sqrt{6}}{5}$

Decimal Form:

0.97979589 \dots

$0.97979589 \dots$