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Higher Roots: example 9.89 · Physics Playground

Exercises Roots and quadratic equations

Example 9.89 from Elementary Algebra, 9.7 Higher Roots

Higher Roots: example 9.89

Simplify: ⓐ $\sqrt[3]{−64}$ ⓑ $\sqrt[4]{−16}$ ⓒ $\sqrt[5]{−243}$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ
  $\begin{matrix} \sqrt[3]{−64} \\ Since {(−4)}^{3} = −64 . & −4 \end{matrix}$
2. ⓑ
  $\begin{matrix} \sqrt[4]{−16} \\ \begin{matrix} Think, {(?)}^{4} = −16 . No real number raised \\ to the fourth power is positive. \end{matrix} & Not a real number. \end{matrix}$
3. ⓒ
  $\begin{matrix} \sqrt[5]{−243} \\ Since {(−3)}^{5} = −243 . & −3 \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: ⓐ $\sqrt[3]{−125}$ ⓑ $\sqrt[4]{−16}$ ⓒ $\sqrt[5]{−32}$ .

How did it go?

PreviousHigher Roots: example 9.88 Next Higher Roots: example 9.90

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 9.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.