Chapter 6.6, Problem 1AGP

To determine

To Write:

  $a^{\frac{1}{5}}$ in radical form.

Answer to Problem 1AGP

  $\sqrt[5]{a}$

Explanation of Solution

Concept Used :

• Definition of nth root:
• Words : For any real numbers a and b , and any positive integer n , if $a^n=b$ then a is the nth root of b . That is $a=\sqrt[n]{b}$

  $\begin{array}{l}\sqrt[n]{b}\\ Here\\ b=radicand\\ n=index\\ \sqrt{}=radicalsign\end{array}$

• For any real number b and any positive inteber n , $b^{\frac{1}{n}}=\sqrt[n]{b}$ , except when b < 0 and n is even. When b < 0 and n is even , a complex root may exist.
• $\sqrt{-1}=i$
• $b^{-n}=\frac{1}{b^n}$

Calculation:

• Given$a^{\frac{1}{5}}$
• $a^{\frac{1}{5}}=\sqrt[5]{a}\mathrm{..............}[{\text{definition of b}}^{\frac{1}{n}}]$