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Higher Roots: example 9.88 · Physics Playground

Exercises Roots and quadratic equations

Example 9.88 from Elementary Algebra, 9.7 Higher Roots

Higher Roots: example 9.88

Simplify: ⓐ $\sqrt[3]{8}$ ⓑ $\sqrt[4]{81}$ ⓒ $\sqrt[5]{32}$ .

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. ⓐ $\begin{matrix} \sqrt[3]{8} \\ Since {(2)}^{3} = 8 . & 2 \end{matrix}$
2. ⓑ
  $\begin{matrix} \sqrt[4]{81} \\ Since {(3)}^{4} = 81 . & 3 \end{matrix}$
3. ⓒ
  $\begin{matrix} \sqrt[5]{32} \\ Since {(2)}^{5} = 32 . & 2 \end{matrix}$

Your turn

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

Simplify: ⓐ $\sqrt[3]{27}$ ⓑ $\sqrt[4]{256}$ ⓒ $\sqrt[5]{243}$ .

How did it go?

PreviousSolve Equations with Square Roots: example 9.87 Next Higher Roots: example 9.89

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.