Basic Math Examples

\frac{16 \div 2^{2}}{\sqrt{18} - 7}

$\frac{16 \div 2^{2}}{\sqrt{18} - 7}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

16 \div 2^{2} \cdot \frac{1}{\sqrt{18} - 7}

$16 \div 2^{2} \cdot \frac{1}{\sqrt{18} - 7}$

Step 2

Rewrite the division as a fraction.

\frac{16}{2^{2}} \cdot \frac{1}{\sqrt{18} - 7}

$\frac{16}{2^{2}} \cdot \frac{1}{\sqrt{18} - 7}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Raise

2

$2$ to the power of

2

$2$ .

\frac{16}{4} \cdot \frac{1}{\sqrt{18} - 7}

$\frac{16}{4} \cdot \frac{1}{\sqrt{18} - 7}$

Step 3.2

Divide

16

$16$ by

4

$4$ .

4 \frac{1}{\sqrt{18} - 7}

$4 \frac{1}{\sqrt{18} - 7}$

4 \frac{1}{\sqrt{18} - 7}

$4 \frac{1}{\sqrt{18} - 7}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Rewrite

18

$18$ as

3^{2} \cdot 2

$3^{2} \cdot 2$ .

Tap for more steps...

Step 4.1.1

Factor

9

$9$ out of

18

$18$ .

4 \frac{1}{\sqrt{9 (2)} - 7}

$4 \frac{1}{\sqrt{9 (2)} - 7}$

Step 4.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

4 \frac{1}{\sqrt{3^{2} \cdot 2} - 7}

$4 \frac{1}{\sqrt{3^{2} \cdot 2} - 7}$

4 \frac{1}{\sqrt{3^{2} \cdot 2} - 7}

$4 \frac{1}{\sqrt{3^{2} \cdot 2} - 7}$

Step 4.2

Pull terms out from under the radical.

4 \frac{1}{3 \sqrt{2} - 7}

$4 \frac{1}{3 \sqrt{2} - 7}$

4 \frac{1}{3 \sqrt{2} - 7}

$4 \frac{1}{3 \sqrt{2} - 7}$

Step 5

Multiply

\frac{1}{3 \sqrt{2} - 7}

$\frac{1}{3 \sqrt{2} - 7}$ by

\frac{3 \sqrt{2} + 7}{3 \sqrt{2} + 7}

$\frac{3 \sqrt{2} + 7}{3 \sqrt{2} + 7}$ .

4 (\frac{1}{3 \sqrt{2} - 7} \cdot \frac{3 \sqrt{2} + 7}{3 \sqrt{2} + 7})

$4 (\frac{1}{3 \sqrt{2} - 7} \cdot \frac{3 \sqrt{2} + 7}{3 \sqrt{2} + 7})$

Step 6

Multiply

\frac{1}{3 \sqrt{2} - 7}

$\frac{1}{3 \sqrt{2} - 7}$ by

\frac{3 \sqrt{2} + 7}{3 \sqrt{2} + 7}

$\frac{3 \sqrt{2} + 7}{3 \sqrt{2} + 7}$ .

4 \frac{3 \sqrt{2} + 7}{(3 \sqrt{2} - 7) (3 \sqrt{2} + 7)}

$4 \frac{3 \sqrt{2} + 7}{(3 \sqrt{2} - 7) (3 \sqrt{2} + 7)}$

Step 7

Expand the denominator using the FOIL method.

4 \frac{3 \sqrt{2} + 7}{9 {\sqrt{2}}^{2} + 21 \sqrt{2} - 21 \sqrt{2} - 49}

$4 \frac{3 \sqrt{2} + 7}{9 {\sqrt{2}}^{2} + 21 \sqrt{2} - 21 \sqrt{2} - 49}$

Step 8

Simplify.

4 \frac{3 \sqrt{2} + 7}{- 31}

$4 \frac{3 \sqrt{2} + 7}{- 31}$

Step 9

Move the negative in front of the fraction.

4 (- \frac{3 \sqrt{2} + 7}{31})

$4 (- \frac{3 \sqrt{2} + 7}{31})$

Step 10

Multiply

4 (- \frac{3 \sqrt{2} + 7}{31})

$4 (- \frac{3 \sqrt{2} + 7}{31})$ .

Tap for more steps...

Step 10.1

Multiply

- 1

$- 1$ by

4

$4$ .

- 4 \frac{3 \sqrt{2} + 7}{31}

$- 4 \frac{3 \sqrt{2} + 7}{31}$

Step 10.2

Combine

- 4

$- 4$ and

\frac{3 \sqrt{2} + 7}{31}

$\frac{3 \sqrt{2} + 7}{31}$ .

\frac{- 4 (3 \sqrt{2} + 7)}{31}

$\frac{- 4 (3 \sqrt{2} + 7)}{31}$

\frac{- 4 (3 \sqrt{2} + 7)}{31}

$\frac{- 4 (3 \sqrt{2} + 7)}{31}$

Step 11

Move the negative in front of the fraction.

- \frac{4 (3 \sqrt{2} + 7)}{31}

$- \frac{4 (3 \sqrt{2} + 7)}{31}$

Step 12

The result can be shown in multiple forms.

Exact Form:

- \frac{4 (3 \sqrt{2} + 7)}{31}

$- \frac{4 (3 \sqrt{2} + 7)}{31}$

Decimal Form:

- 1.45066331 \dots

$- 1.45066331 \dots$