Basic Math Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Rewrite the division as a fraction.

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

Step 3

Simplify the expression.

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Step 3.1

Raise $2$ to the power of $2$ .

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

Step 3.2

Divide $16$ by $4$ .

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

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 4.1.1

Factor $9$ out of $18$ .

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

Step 4.1.2

Rewrite $9$ as $3^{2}$ .

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

Step 4.2

Pull terms out from under the radical.

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

Step 5

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

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

Step 6

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

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

Step 7

Expand the denominator using the FOIL method.

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

Step 8

Simplify.

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

Step 9

Move the negative in front of the fraction.

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

Step 10

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

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Step 10.1

Multiply $- 1$ by $4$ .

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

Step 10.2

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

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

Step 11

Move the negative in front of the fraction.

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

Step 12

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 1.45066331 \dots$