Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Raise $- 7$ to the power of $2$ .

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

Step 1.2

Raise $- 7$ to the power of $2$ .

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

Step 1.3

Add $49$ and $49$ .

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

Step 1.4

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.4.1

Factor $49$ out of $98$ .

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

Step 1.4.2

Rewrite $49$ as $7^{2}$ .

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

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

Step 1.5

Pull terms out from under the radical.

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

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

Step 2

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.09994388 \dots$

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