Basic Math Examples

$2 \sqrt{18} - \sqrt{4} + \sqrt{8}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Factor $9$ out of $18$ .

$2 \sqrt{9 (2)} - \sqrt{4} + \sqrt{8}$

Step 1.1.2

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

$2 \sqrt{3^{2} \cdot 2} - \sqrt{4} + \sqrt{8}$

$2 \sqrt{3^{2} \cdot 2} - \sqrt{4} + \sqrt{8}$

Step 1.2

Pull terms out from under the radical.

$2 (3 \sqrt{2}) - \sqrt{4} + \sqrt{8}$

Step 1.3

Multiply $3$ by $2$ .

$6 \sqrt{2} - \sqrt{4} + \sqrt{8}$

Step 1.4

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

$6 \sqrt{2} - \sqrt{2^{2}} + \sqrt{8}$

Step 1.5

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

$6 \sqrt{2} - 1 \cdot 2 + \sqrt{8}$

Step 1.6

Multiply $- 1$ by $2$ .

$6 \sqrt{2} - 2 + \sqrt{8}$

Step 1.7

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 1.7.1

Factor $4$ out of $8$ .

$6 \sqrt{2} - 2 + \sqrt{4 (2)}$

Step 1.7.2

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

$6 \sqrt{2} - 2 + \sqrt{2^{2} \cdot 2}$

$6 \sqrt{2} - 2 + \sqrt{2^{2} \cdot 2}$

Step 1.8

Pull terms out from under the radical.

$6 \sqrt{2} - 2 + 2 \sqrt{2}$

$6 \sqrt{2} - 2 + 2 \sqrt{2}$

Step 2

Add $6 \sqrt{2}$ and $2 \sqrt{2}$ .

$- 2 + 8 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 2 + 8 \sqrt{2}$

Decimal Form:

$9.31370849 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$