Precalculus Examples

\sqrt{49 x^{2} + 49}

$\sqrt{49 x^{2} + 49}$

Step 1

Factor

49

$49$ out of

49 x^{2} + 49

$49 x^{2} + 49$ .

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Step 1.1

Factor

49

$49$ out of

49 x^{2}

$49 x^{2}$ .

\sqrt{49 (x^{2}) + 49}

$\sqrt{49 (x^{2}) + 49}$

Step 1.2

Factor

49

$49$ out of

49

$49$ .

\sqrt{49 (x^{2}) + 49 (1)}

$\sqrt{49 (x^{2}) + 49 (1)}$

Step 1.3

Factor

49

$49$ out of

49 (x^{2}) + 49 (1)

$49 (x^{2}) + 49 (1)$ .

\sqrt{49 (x^{2} + 1)}

$\sqrt{49 (x^{2} + 1)}$

\sqrt{49 (x^{2} + 1)}

$\sqrt{49 (x^{2} + 1)}$

Step 2

Rewrite

49 (x^{2} + 1)

$49 (x^{2} + 1)$ as

7^{2} (x^{2} + 1^{2})

$7^{2} (x^{2} + 1^{2})$ .

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Step 2.1

Rewrite

49

$49$ as

7^{2}

$7^{2}$ .

\sqrt{7^{2} (x^{2} + 1)}

$\sqrt{7^{2} (x^{2} + 1)}$

Step 2.2

Rewrite

1

$1$ as

$1^{2}$ .

$\sqrt{7^{2} (x^{2} + 1^{2})}$

$\sqrt{7^{2} (x^{2} + 1^{2})}$

Step 3

Pull terms out from under the radical.

$7 \sqrt{x^{2} + 1^{2}}$

Step 4

One to any power is one.

$7 \sqrt{x^{2} + 1}$

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