Basic Math Examples

$c^{2} = {(\sqrt{6})}^{2} + 3^{2}$

Step 1

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

$c = \pm \sqrt{{\sqrt{6}}^{2} + 3^{2}}$

Step 2

Simplify $\pm \sqrt{{\sqrt{6}}^{2} + 3^{2}}$ .

Tap for more steps...

Step 2.1

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Tap for more steps...

Step 2.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$c = \pm \sqrt{{(6^{\frac{1}{2}})}^{2} + 3^{2}}$

Step 2.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$c = \pm \sqrt{6^{\frac{1}{2} \cdot 2} + 3^{2}}$

Step 2.1.3

Combine $\frac{1}{2}$ and $2$ .

$c = \pm \sqrt{6^{\frac{2}{2}} + 3^{2}}$

Step 2.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.4.1

Cancel the common factor.

$c = \pm \sqrt{6^{\frac{2}{2}} + 3^{2}}$

Step 2.1.4.2

Rewrite the expression.

$c = \pm \sqrt{6^{1} + 3^{2}}$

Step 2.1.5

Evaluate the exponent.

$c = \pm \sqrt{6 + 3^{2}}$

Step 2.2

Simplify the expression.

Tap for more steps...

Step 2.2.1

Raise $3$ to the power of $2$ .

$c = \pm \sqrt{6 + 9}$

Step 2.2.2

Add $6$ and $9$ .

$c = \pm \sqrt{15}$

Step 3

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

Tap for more steps...

Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$c = \sqrt{15}$

Step 3.2

Next, use the negative value of the $\pm$ to find the second solution.

$c = - \sqrt{15}$

Step 3.3

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

$c = \sqrt{15}, - \sqrt{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \sqrt{15}, - \sqrt{15}$

Decimal Form:

$c = 3.87298334 \dots, - 3.87298334 \dots$