Precalculus Examples

\frac{\sqrt{{(- 7)}^{2} + {(- 7)}^{2}}}{{(3)}^{2}}

$\frac{\sqrt{{(- 7)}^{2} + {(- 7)}^{2}}}{{(3)}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise

- 7

$- 7$ to the power of

2

$2$ .

\frac{\sqrt{49 + {(- 7)}^{2}}}{3^{2}}

$\frac{\sqrt{49 + {(- 7)}^{2}}}{3^{2}}$

Step 1.2

Raise

- 7

$- 7$ to the power of

2

$2$ .

\frac{\sqrt{49 + 49}}{3^{2}}

$\frac{\sqrt{49 + 49}}{3^{2}}$

Step 1.3

Add

49

$49$ and

49

$49$ .

\frac{\sqrt{98}}{3^{2}}

$\frac{\sqrt{98}}{3^{2}}$

Step 1.4

Rewrite

98

$98$ as

7^{2} \cdot 2

$7^{2} \cdot 2$ .

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Step 1.4.1

Factor

49

$49$ out of

98

$98$ .

\frac{\sqrt{49 (2)}}{3^{2}}

$\frac{\sqrt{49 (2)}}{3^{2}}$

Step 1.4.2

Rewrite

49

$49$ as

7^{2}

$7^{2}$ .

\frac{\sqrt{7^{2} \cdot 2}}{3^{2}}

$\frac{\sqrt{7^{2} \cdot 2}}{3^{2}}$

\frac{\sqrt{7^{2} \cdot 2}}{3^{2}}

$\frac{\sqrt{7^{2} \cdot 2}}{3^{2}}$

Step 1.5

Pull terms out from under the radical.

\frac{7 \sqrt{2}}{3^{2}}

$\frac{7 \sqrt{2}}{3^{2}}$

\frac{7 \sqrt{2}}{3^{2}}

$\frac{7 \sqrt{2}}{3^{2}}$

Step 2

Raise

3

$3$ to the power of

2

$2$ .

\frac{7 \sqrt{2}}{9}

$\frac{7 \sqrt{2}}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{7 \sqrt{2}}{9}

$\frac{7 \sqrt{2}}{9}$

Decimal Form:

1.09994388 \dots

$1.09994388 \dots$

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

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