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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 524. (page 1143)

Write as a radical expression:
a) $x^{\frac{1}{2}}$
b) role="math" localid="1650392359303" $y^{\frac{1}{4}}$
c) $z^{\frac{1}{4}}$

Short Answer

Expert verified

a) $x^{\frac{1}{2}} = \sqrt{x}$

b) localid="1650439728314" $y^{\frac{1}{4}} = \sqrt[4]{y}$

c) $z^{\frac{1}{4}} = \sqrt[4]{z}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is $x^{\frac{1}{2}}$ .

02

Part (a) Step 2: Simplification

We want to write expression of the form $\sqrt[n]{a}$ .

The denominator of radical is $2$ , so the index of radical is $2$ . We do not show index in this case.

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

03

Part (b) Step 1: Given Information

The given expression is $y^{\frac{1}{4}}$ .

04

Part (b) Step 2: Simplification

The denominator of the index is 4. So the exponent is 4.

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

05

Part (c) Step 1: Given Information

The given expression is $z^{\frac{1}{4}}$ .

06

Part (c) Step 2: Simplification

The denominator of exponent is $4$ . So the index is $4$ .

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

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