Calculus Examples

$\sqrt{10^{2} + {(- 5)}^{2}}$

Step 1

Raise $10$ to the power of $2$ .

$\sqrt{100 + {(- 5)}^{2}}$

Step 2

Raise $- 5$ to the power of $2$ .

$\sqrt{100 + 25}$

Step 3

Add $100$ and $25$ .

$\sqrt{125}$

Step 4

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 4.1

Factor $25$ out of $125$ .

$\sqrt{25 (5)}$

Step 4.2

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

$\sqrt{5^{2} \cdot 5}$

$\sqrt{5^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$5 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5}$

Decimal Form:

$11.18033988 \dots$

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