Precalculus Examples

\sqrt{9 a^{3}} + \sqrt{a}

$\sqrt{9 a^{3}} + \sqrt{a}$

Step 1

Rewrite

9 a^{3}

$9 a^{3}$ as

{(3 a)}^{2} a

${(3 a)}^{2} a$ .

Tap for more steps...

Step 1.1

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\sqrt{3^{2} a^{3}} + \sqrt{a}

$\sqrt{3^{2} a^{3}} + \sqrt{a}$

Step 1.2

Factor out

a^{2}

$a^{2}$ .

\sqrt{3^{2} (a^{2} a)} + \sqrt{a}

$\sqrt{3^{2} (a^{2} a)} + \sqrt{a}$

Step 1.3

Rewrite

3^{2} a^{2}

$3^{2} a^{2}$ as

{(3 a)}^{2}

${(3 a)}^{2}$ .

\sqrt{{(3 a)}^{2} a} + \sqrt{a}

$\sqrt{{(3 a)}^{2} a} + \sqrt{a}$

\sqrt{{(3 a)}^{2} a} + \sqrt{a}

$\sqrt{{(3 a)}^{2} a} + \sqrt{a}$

Step 2

Pull terms out from under the radical.

3 a \sqrt{a} + \sqrt{a}

$3 a \sqrt{a} + \sqrt{a}$

$\sqrt[]{9 a^{3}} + \sqrt[]{a}$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$