Basic Math Examples

$\sqrt{\frac{100}{16}}$

Step 1

Cancel the common factor of

$100$ and

$16$ .

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Step 1.1

Factor

$4$ out of

$100$ .

$\sqrt{\frac{4 (25)}{16}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

$4$ out of

$16$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Rewrite

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

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

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

Step 3

Simplify the numerator.

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Step 3.1

Rewrite

$25$ as

$5^{2}$ .

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

Step 3.2

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

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

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

$4$ as

$2^{2}$ .

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

Step 4.2

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

$\frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$