Algebra Examples

$f (- 8) = \sqrt{- 8^{2} + 1}$

Step 1

Simplify the expression.

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Step 1.1

Raise $8$ to the power of $2$ .

$f (- 8) = \sqrt{- 1 \cdot 64 + 1}$

Step 1.2

Multiply $- 1$ by $64$ .

$f (- 8) = \sqrt{- 64 + 1}$

Step 1.3

Add $- 64$ and $1$ .

$f (- 8) = \sqrt{- 63}$

$f (- 8) = \sqrt{- 63}$

Step 2

Rewrite $- 63$ as $- 1 (63)$ .

$f (- 8) = \sqrt{- 1 \cdot 63}$

Step 3

Rewrite $\sqrt{- 1 (63)}$ as $\sqrt{- 1} \cdot \sqrt{63}$ .

$f (- 8) = \sqrt{- 1} \cdot \sqrt{63}$

Step 4

Rewrite $\sqrt{- 1}$ as $i$ .

$f (- 8) = i \cdot \sqrt{63}$

Step 5

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 5.1

Factor $9$ out of $63$ .

$f (- 8) = i \cdot \sqrt{9 (7)}$

Step 5.2

Rewrite $9$ as $3^{2}$ .

$f (- 8) = i \cdot \sqrt{3^{2} \cdot 7}$

$f (- 8) = i \cdot \sqrt{3^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

$f (- 8) = i \cdot (3 \sqrt{7})$

Step 7

Move $3$ to the left of $i$ .

$f (- 8) = 3 i \sqrt{7}$

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