Finite Math Examples

$\sqrt{\frac{100}{64}}$

Step 1

Cancel the common factor of $100$ and $64$ .

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Step 1.1

Factor $4$ out of $100$ .

$\sqrt{\frac{4 (25)}{64}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $64$ .

$\sqrt{\frac{4 \cdot 25}{4 \cdot 16}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{4 \cdot 25}{4 \cdot 16}}$

Step 1.2.3

Rewrite the expression.

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

Step 2

Rewrite $\sqrt{\frac{25}{16}}$ as $\frac{\sqrt{25}}{\sqrt{16}}$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{\sqrt{5^{2}}}{\sqrt{16}}$

Step 3.2

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

$\frac{5}{\sqrt{16}}$

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

$\frac{5}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$