Precalculus Examples

$\sqrt{81 x^{2} + 81}$

Step 1

Factor $81$ out of $81 x^{2} + 81$ .

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Step 1.1

Factor $81$ out of $81 x^{2}$ .

$\sqrt{81 (x^{2}) + 81}$

Step 1.2

Factor $81$ out of $81$ .

$\sqrt{81 (x^{2}) + 81 (1)}$

Step 1.3

Factor $81$ out of $81 (x^{2}) + 81 (1)$ .

$\sqrt{81 (x^{2} + 1)}$

Step 2

Rewrite $81 (x^{2} + 1)$ as ${(3^{2})}^{2} (x^{2} + 1)$ .

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Step 2.1

Rewrite $81$ as $9^{2}$ .

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

Step 2.2

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

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

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