Algebra Examples

$\frac{\sqrt{7}}{\sqrt{10} - \sqrt{2}}$

Step 1

Multiply $\frac{\sqrt{7}}{\sqrt{10} - \sqrt{2}}$ by $\frac{\sqrt{10} + \sqrt{2}}{\sqrt{10} + \sqrt{2}}$ .

$\frac{\sqrt{7}}{\sqrt{10} - \sqrt{2}} \cdot \frac{\sqrt{10} + \sqrt{2}}{\sqrt{10} + \sqrt{2}}$

Step 2

Multiply $\frac{\sqrt{7}}{\sqrt{10} - \sqrt{2}}$ by $\frac{\sqrt{10} + \sqrt{2}}{\sqrt{10} + \sqrt{2}}$ .

$\frac{\sqrt{7} (\sqrt{10} + \sqrt{2})}{(\sqrt{10} - \sqrt{2}) (\sqrt{10} + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{7} (\sqrt{10} + \sqrt{2})}{{\sqrt{10}}^{2} + \sqrt{20} - \sqrt{20} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{\sqrt{7} (\sqrt{10} + \sqrt{2})}{8}$

Step 5

Apply the distributive property.

$\frac{\sqrt{7} \sqrt{10} + \sqrt{7} \sqrt{2}}{8}$

Step 6

Combine using the product rule for radicals.

$\frac{\sqrt{7 \cdot 10} + \sqrt{7} \sqrt{2}}{8}$

Step 7

Combine using the product rule for radicals.

$\frac{\sqrt{7 \cdot 10} + \sqrt{7 \cdot 2}}{8}$

Step 8

Simplify each term.

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Step 8.1

Multiply $7$ by $10$ .

$\frac{\sqrt{70} + \sqrt{7 \cdot 2}}{8}$

Step 8.2

Multiply $7$ by $2$ .

$\frac{\sqrt{70} + \sqrt{14}}{8}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{70} + \sqrt{14}}{8}$

Decimal Form:

$1.51353220 \dots$