Basic Math Examples

$\sqrt{(\frac{5}{8} - \frac{9}{16}) \div (1 + \frac{9}{16})}$

Step 1

To write $\frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{(\frac{5}{8} \cdot \frac{2}{2} - \frac{9}{16}) \div (1 + \frac{9}{16})}$

Step 2

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.1

Multiply $\frac{5}{8}$ by $\frac{2}{2}$ .

$\sqrt{(\frac{5 \cdot 2}{8 \cdot 2} - \frac{9}{16}) \div (1 + \frac{9}{16})}$

Step 2.2

Multiply $8$ by $2$ .

$\sqrt{(\frac{5 \cdot 2}{16} - \frac{9}{16}) \div (1 + \frac{9}{16})}$

Step 3

Combine the numerators over the common denominator.

$\sqrt{\frac{5 \cdot 2 - 9}{16} \div (1 + \frac{9}{16})}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply $5$ by $2$ .

$\sqrt{\frac{10 - 9}{16} \div (1 + \frac{9}{16})}$

Step 4.2

Subtract $9$ from $10$ .

$\sqrt{\frac{1}{16} \div (1 + \frac{9}{16})}$

Step 5

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{1}{16} \div (\frac{16}{16} + \frac{9}{16})}$

Step 6

Combine the numerators over the common denominator.

$\sqrt{\frac{1}{16} \div \frac{16 + 9}{16}}$

Step 7

Add $16$ and $9$ .

$\sqrt{\frac{1}{16} \div \frac{25}{16}}$

Step 8

To divide by a fraction, multiply by its reciprocal.

$\sqrt{\frac{1}{16} \cdot \frac{16}{25}}$

Step 9

Cancel the common factor of $16$ .

Tap for more steps...

Step 9.1

Cancel the common factor.

$\sqrt{\frac{1}{16} \cdot \frac{16}{25}}$

Step 9.2

Rewrite the expression.

$\sqrt{\frac{1}{25}}$

Step 10

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

$\frac{\sqrt{1}}{\sqrt{25}}$

Step 11

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{25}}$

Step 12

Simplify the denominator.

Tap for more steps...

Step 12.1

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

$\frac{1}{\sqrt{5^{2}}}$

Step 12.2

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

$\frac{1}{5}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$