Calculus Examples

$f (6) = \sqrt{64 - x^{2}}$

Step 1

Replace the variable $x$ with $6$ in the expression.

$f (6) = \sqrt{64 - {(6)}^{2}}$

Step 2

Simplify the result.

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Step 2.1

Raise $6$ to the power of $2$ .

$f (6) = \sqrt{64 - 1 \cdot 36}$

Step 2.2

Multiply $- 1$ by $36$ .

$f (6) = \sqrt{64 - 36}$

Step 2.3

Subtract $36$ from $64$ .

$f (6) = \sqrt{28}$

Step 2.4

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 2.4.1

Factor $4$ out of $28$ .

$f (6) = \sqrt{4 (7)}$

Step 2.4.2

Rewrite $4$ as $2^{2}$ .

$f (6) = \sqrt{2^{2} \cdot 7}$

$f (6) = \sqrt{2^{2} \cdot 7}$

Step 2.5

Pull terms out from under the radical.

$f (6) = 2 \sqrt{7}$

Step 2.6

The final answer is $2 \sqrt{7}$ .

$2 \sqrt{7}$

$2 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{7}$

Decimal Form:

$5.29150262 \dots$

Step 4

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