Pre-Algebra Examples

$\sqrt{\frac{5}{16}} - \sqrt{\frac{5}{64}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt{\frac{5}{16}}$ as $\frac{\sqrt{5}}{\sqrt{16}}$ .

$\frac{\sqrt{5}}{\sqrt{16}} - \sqrt{\frac{5}{64}}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

$\frac{\sqrt{5}}{\sqrt{4^{2}}} - \sqrt{\frac{5}{64}}$

Step 1.2.2

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

$\frac{\sqrt{5}}{4} - \sqrt{\frac{5}{64}}$

Step 1.3

Rewrite $\sqrt{\frac{5}{64}}$ as $\frac{\sqrt{5}}{\sqrt{64}}$ .

$\frac{\sqrt{5}}{4} - \frac{\sqrt{5}}{\sqrt{64}}$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Rewrite $64$ as $8^{2}$ .

$\frac{\sqrt{5}}{4} - \frac{\sqrt{5}}{\sqrt{8^{2}}}$

Step 1.4.2

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

$\frac{\sqrt{5}}{4} - \frac{\sqrt{5}}{8}$

Step 2

To write $\frac{\sqrt{5}}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\sqrt{5}}{4} \cdot \frac{2}{2} - \frac{\sqrt{5}}{8}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{\sqrt{5}}{4}$ by $\frac{2}{2}$ .

$\frac{\sqrt{5} \cdot 2}{4 \cdot 2} - \frac{\sqrt{5}}{8}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{\sqrt{5} \cdot 2}{8} - \frac{\sqrt{5}}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{\sqrt{5} \cdot 2 - \sqrt{5}}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Move $2$ to the left of $\sqrt{5}$ .

$\frac{2 \cdot \sqrt{5} - \sqrt{5}}{8}$

Step 5.2

Subtract $\sqrt{5}$ from $2 \sqrt{5}$ .

$\frac{\sqrt{5}}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{5}}{8}$

Decimal Form:

$0.27950849 \dots$