Precalculus Examples

$\sqrt{25 x^{2} + 25}$

Step 1

Factor $25$ out of $25 x^{2} + 25$ .

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Step 1.1

Factor $25$ out of $25 x^{2}$ .

$\sqrt{25 (x^{2}) + 25}$

Step 1.2

Factor $25$ out of $25$ .

$\sqrt{25 (x^{2}) + 25 (1)}$

Step 1.3

Factor $25$ out of $25 (x^{2}) + 25 (1)$ .

$\sqrt{25 (x^{2} + 1)}$

Step 2

Rewrite $25 (x^{2} + 1)$ as $5^{2} (x^{2} + 1^{2})$ .

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} (x^{2} + 1)}$

Step 2.2

Rewrite $1$ as $1^{2}$ .

$\sqrt{5^{2} (x^{2} + 1^{2})}$

Step 3

Pull terms out from under the radical.

$5 \sqrt{x^{2} + 1^{2}}$

Step 4

One to any power is one.

$5 \sqrt{x^{2} + 1}$