Algebra Examples

$\frac{2}{\sqrt{8} + \sqrt{7}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

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

$\frac{2}{\sqrt{2^{2} \cdot 2} + \sqrt{7}}$

Step 1.2

Pull terms out from under the radical.

$\frac{2}{| 2 | \sqrt{2} + \sqrt{7}}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 2

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

$\frac{2}{2 \sqrt{2} + \sqrt{7}} \cdot \frac{2 \sqrt{2} - \sqrt{7}}{2 \sqrt{2} - \sqrt{7}}$

Step 3

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

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

Step 4

Expand the denominator using the FOIL method.

$\frac{2 (2 \sqrt{2} - \sqrt{7})}{4 {\sqrt{2}}^{2} - 2 \sqrt{14} + 2 \sqrt{14} - {\sqrt{7}}^{2}}$

Step 5

Simplify.

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

Step 6

Divide $2 (2 \sqrt{2} - \sqrt{7})$ by $1$ .

$2 (2 \sqrt{2} - \sqrt{7})$

Step 7

Apply the distributive property.

$2 (2 \sqrt{2}) + 2 (- \sqrt{7})$

Step 8

Multiply $2$ by $2$ .

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

Step 9

Multiply $- 1$ by $2$ .

$4 \sqrt{2} - 2 \sqrt{7}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2} - 2 \sqrt{7}$

Decimal Form:

$0.36535162 \dots$