Precalculus Examples

$f (n) = \sqrt[4]{5 n - 231}$ ; find $f (- 5)$

Step 1

Replace the variable $n$ with $- 5$ in the expression.

$f (- 5) = \sqrt[4]{5 (- 5) - 231}$

Step 2

Simplify $\sqrt[4]{5 (- 5) - 231}$ .

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Step 2.1

Remove parentheses.

$\sqrt[4]{5 (- 5) - 231}$

Step 2.2

Multiply $5$ by $- 5$ .

$\sqrt[4]{- 25 - 231}$

Step 2.3

Subtract $231$ from $- 25$ .

$\sqrt[4]{- 256}$

Step 2.4

Rewrite $- 256$ as $4^{4} \cdot - 1$ .

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Step 2.4.1

Factor $256$ out of $- 256$ .

$\sqrt[4]{256 (- 1)}$

Step 2.4.2

Rewrite $256$ as $4^{4}$ .

$\sqrt[4]{4^{4} \cdot - 1}$

Step 2.5

Pull terms out from under the radical.

$4 \sqrt[4]{- 1}$