Calculus Examples

$f (x) = \sqrt{x^{2} + 11}$ , $x = 5$

Step 1

Replace the variable $x$ with $5$ in the expression.

$f (5) = \sqrt{{(5)}^{2} + 11}$

Step 2

Simplify the result.

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Step 2.1

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

$f (5) = \sqrt{25 + 11}$

Step 2.2

Add $25$ and $11$ .

$f (5) = \sqrt{36}$

Step 2.3

Rewrite $36$ as $6^{2}$ .

$f (5) = \sqrt{6^{2}}$

Step 2.4

Pull terms out from under the radical, assuming positive real numbers.

$f (5) = 6$

Step 2.5

The final answer is $6$ .

$6$

Step 3