Chapter 8: Q. 119 (page 786)

In the following exercise, write as a radical expression.
$ⓐ x^{\frac{1}{2}} ⓑ y^{\frac{1}{3}} ⓒ z^{\frac{1}{4}}$

Short Answer

Expert verified

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

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

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

Step by step solution

Part (a) Step 1. Radical expression of x12

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,

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

Part (b). Radical expression of y13

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

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

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

Part (c) Radical expression of z14

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

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

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

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In the following exercise, write as a radical expression.
$ⓐ x^{\frac{1}{2}} ⓑ y^{\frac{1}{3}} ⓒ z^{\frac{1}{4}}$

Short Answer

Step by step solution

Part (a) Step 1. Radical expression of x12

Part (b). Radical expression of y13

Part (c) Radical expression of z14

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In the following exercise, write as a radical expression.ⓐx12ⓑy13ⓒz14

Short Answer

Step by step solution

Part (a) Step 1. Radical expression of x12

Part (b). Radical expression of y13

Part (c) Radical expression of z14

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Calculus

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercise, write as a radical expression.
$ⓐ x^{\frac{1}{2}} ⓑ y^{\frac{1}{3}} ⓒ z^{\frac{1}{4}}$