Basic Math Examples

$\frac{1}{(\sqrt{3} + \sqrt{2}) (\sqrt[4]{3} + \sqrt[4]{2})}$

Step 1

Multiply $\frac{1}{(\sqrt{3} + \sqrt{2}) (\sqrt[4]{3} + \sqrt[4]{2})}$ by $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ .

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

Step 2

Multiply $\frac{1}{(\sqrt{3} + \sqrt{2}) (\sqrt[4]{3} + \sqrt[4]{2})}$ by $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ .

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

Step 3

Simplify the expression.

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Step 3.1

Move $\sqrt{3} + \sqrt{2}$ .

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

Step 3.2

Expand the denominator using the FOIL method.

$\frac{\sqrt{3} - \sqrt{2}}{(\sqrt[4]{3} + \sqrt[4]{2}) ({\sqrt{3}}^{2} - \sqrt{6} + \sqrt{6} - {\sqrt{2}}^{2})}$

Step 3.3

Simplify.

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

Step 3.4

Multiply $\sqrt[4]{3} + \sqrt[4]{2}$ by $1$ .

$\frac{\sqrt{3} - \sqrt{2}}{\sqrt[4]{3} + \sqrt[4]{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3} - \sqrt{2}}{\sqrt[4]{3} + \sqrt[4]{2}}$

Decimal Form:

$0.12686689 \dots$