Algebra Examples

x^{2} = \sqrt{3}

$x^{2} = \sqrt{3}$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x = \pm \sqrt{\sqrt{3}}

$x = \pm \sqrt{\sqrt{3}}$

Step 2

Rewrite

\sqrt{\sqrt{3}}

$\sqrt{\sqrt{3}}$ as

\sqrt[4]{3}

$\sqrt[4]{3}$ .

x = \pm \sqrt[4]{3}

$x = \pm \sqrt[4]{3}$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

x = \sqrt[4]{3}

$x = \sqrt[4]{3}$

Step 3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - \sqrt[4]{3}

$x = - \sqrt[4]{3}$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

x = \sqrt[4]{3}, - \sqrt[4]{3}

$x = \sqrt[4]{3}, - \sqrt[4]{3}$

x = \sqrt[4]{3}, - \sqrt[4]{3}

$x = \sqrt[4]{3}, - \sqrt[4]{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \sqrt[4]{3}, - \sqrt[4]{3}

$x = \sqrt[4]{3}, - \sqrt[4]{3}$

Decimal Form:

x = 1.31607401 \dots, - 1.31607401 \dots

$x = 1.31607401 \dots, - 1.31607401 \dots$