Algebra Examples

$\frac{1}{2 - \sqrt[4]{9}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{1}{2 - \sqrt[4]{3^{2}}}$

Step 1.2

Rewrite $\sqrt[4]{3^{2}}$ as $\sqrt{\sqrt{3^{2}}}$ .

$\frac{1}{2 - \sqrt{\sqrt{3^{2}}}}$

Step 1.3

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

$\frac{1}{2 - \sqrt{3}}$

Step 2

Multiply $\frac{1}{2 - \sqrt{3}}$ by $\frac{2 + \sqrt{3}}{2 + \sqrt{3}}$ .

$\frac{1}{2 - \sqrt{3}} \cdot \frac{2 + \sqrt{3}}{2 + \sqrt{3}}$

Step 3

Multiply $\frac{1}{2 - \sqrt{3}}$ by $\frac{2 + \sqrt{3}}{2 + \sqrt{3}}$ .

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

Step 4

Expand the denominator using the FOIL method.

$\frac{2 + \sqrt{3}}{4 + 2 \sqrt{3} - 2 \sqrt{3} - {\sqrt{3}}^{2}}$

Step 5

Simplify.

$\frac{2 + \sqrt{3}}{1}$

Step 6

Divide $2 + \sqrt{3}$ by $1$ .

$2 + \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2 + \sqrt{3}$

Decimal Form:

$3.73205080 \dots$