Precalculus Examples

$f (w) = \sqrt{5 w - 101}$ ; find $f (4)$

Step 1

Replace the variable $w$ with $4$ in the expression.

$f (4) = \sqrt{5 (4) - 101}$

Step 2

Simplify $\sqrt{5 (4) - 101}$ .

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Step 2.1

Simplify the expression.

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Step 2.1.1

Remove parentheses.

$\sqrt{5 (4) - 101}$

Step 2.1.2

Multiply $5$ by $4$ .

$\sqrt{20 - 101}$

Step 2.1.3

Subtract $101$ from $20$ .

$\sqrt{- 81}$

Step 2.2

Rewrite $- 81$ as $- 1 (81)$ .

$\sqrt{- 1 (81)}$

Step 2.3

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\sqrt{- 1} \cdot \sqrt{81}$

Step 2.4

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

$i \cdot \sqrt{81}$

Step 2.5

Rewrite $81$ as $9^{2}$ .

$i \cdot \sqrt{9^{2}}$

Step 2.6

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

$i \cdot 9$

Step 2.7

Move $9$ to the left of $i$ .

$9 i$