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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 120 (page 1069)

In the following exercises, write as a radical expression.
$鈸� r^{\frac{1}{2}} 鈸� s^{\frac{1}{3}} 鈸� t^{\frac{1}{4}}$

Short Answer

Expert verified

Part (a). $r^{\frac{1}{2}} = \sqrt{r}$

Part (b). $s^{\frac{1}{3}} = \sqrt[3]{s}$

part (c). $t^{\frac{1}{4}} = \sqrt[4]{t}$

Step by step solution

01

Part (a) Step 1. Radical expression of r12

We know that, $a^{\frac{1}{n}} = \sqrt[n]{a}$

The denominator of the rational exponent is $2$ , so the index of the radical is $2$ . We do not show the index when it is $2$ .

So,

$r^{\frac{1}{2}} = \sqrt{r}$

02

Part (b). Radical expression of s13

We know that, $a^{\frac{1}{n}} = \sqrt[n]{a}$

The denominator of the exponent is $3$ , so the index is $3$ .

$s^{\frac{1}{3}} = \sqrt[3]{s}$

03

Part (c) Radical expression of t14

We know that, $a^{\frac{1}{n}} = \sqrt[n]{a}$

The denominator of the exponent is $4$ , so the index is $4$ .

$t^{\frac{1}{4}} = \sqrt[4]{t}$

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Most popular questions from this chapter

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