Pre-Algebra Examples

$\frac{5}{\sqrt{17} - \sqrt{14}}$

Step 1

Multiply $\frac{5}{\sqrt{17} - \sqrt{14}}$ by $\frac{\sqrt{17} + \sqrt{14}}{\sqrt{17} + \sqrt{14}}$ .

$\frac{5}{\sqrt{17} - \sqrt{14}} \cdot \frac{\sqrt{17} + \sqrt{14}}{\sqrt{17} + \sqrt{14}}$

Step 2

Multiply $\frac{5}{\sqrt{17} - \sqrt{14}}$ by $\frac{\sqrt{17} + \sqrt{14}}{\sqrt{17} + \sqrt{14}}$ .

$\frac{5 (\sqrt{17} + \sqrt{14})}{(\sqrt{17} - \sqrt{14}) (\sqrt{17} + \sqrt{14})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (\sqrt{17} + \sqrt{14})}{{\sqrt{17}}^{2} + \sqrt{238} - \sqrt{238} - {\sqrt{14}}^{2}}$

Step 4

Simplify.

$\frac{5 (\sqrt{17} + \sqrt{14})}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (\sqrt{17} + \sqrt{14})}{3}$

Decimal Form:

$13.10793835 \dots$