Precalculus Examples

\sqrt{9 x^{2} + 9}

$\sqrt{9 x^{2} + 9}$

Step 1

Factor

9

$9$ out of

9 x^{2} + 9

$9 x^{2} + 9$ .

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Step 1.1

Factor

9

$9$ out of

9 x^{2}

$9 x^{2}$ .

\sqrt{9 (x^{2}) + 9}

$\sqrt{9 (x^{2}) + 9}$

Step 1.2

Factor

9

$9$ out of

9

$9$ .

\sqrt{9 (x^{2}) + 9 (1)}

$\sqrt{9 (x^{2}) + 9 (1)}$

Step 1.3

Factor

9

$9$ out of

9 (x^{2}) + 9 (1)

$9 (x^{2}) + 9 (1)$ .

\sqrt{9 (x^{2} + 1)}

$\sqrt{9 (x^{2} + 1)}$

\sqrt{9 (x^{2} + 1)}

$\sqrt{9 (x^{2} + 1)}$

Step 2

Rewrite

9 (x^{2} + 1)

$9 (x^{2} + 1)$ as

3^{2} (x^{2} + 1^{2})

$3^{2} (x^{2} + 1^{2})$ .

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Step 2.1

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\sqrt{3^{2} (x^{2} + 1)}

$\sqrt{3^{2} (x^{2} + 1)}$

Step 2.2

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

\sqrt{3^{2} (x^{2} + 1^{2})}

$\sqrt{3^{2} (x^{2} + 1^{2})}$

\sqrt{3^{2} (x^{2} + 1^{2})}

$\sqrt{3^{2} (x^{2} + 1^{2})}$

Step 3

Pull terms out from under the radical.

3 \sqrt{x^{2} + 1^{2}}

$3 \sqrt{x^{2} + 1^{2}}$

Step 4

One to any power is one.

3 \sqrt{x^{2} + 1}

$3 \sqrt{x^{2} + 1}$

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

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