/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 243 (a) Explain why (-n)2聽is always... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q. 243 (page 799)

(a) Explain why (-n)2is always non-negative, for n鈮�0

(b) Explain why -(n)2 is always non-positive, for n鈮�0

Short Answer

Expert verified

(a) (-n)2is always non-negative for n鈮�0since the square is applicable to both negative sign and radical, so negative sign becomes positive and the resultant is non-negative number.

(b) -(n)2is always non-positive for n鈮�0, since the square is only applicable to radical and not negative sign. So the resultant is non-positive number.

Step by step solution

01

Part (a) Step 1. To explain

To explain why (-n)2 is non-negative for n鈮�0

02

Part (a) Step 2. Consider a number

Consider a number n鈮�0

That is n=5

(-n)2=(-5)2

The square is applicable to both negative sign and the radical. So,

=(-5)(-5)

=5which is a non-negative number.

So, for any n鈮�0, (-n)2 is non-negative..

03

Part (b) Step 1. To explain

To explain why -(n)2 is non-positive.

04

Part (b) Step 4. Consider a number.

Consider a number n鈮�0

That is 5

-(n)2=-(5)2

The root is applicable only to radical.

=-(5)(5)

=-(5)which is a negative number.

So, for any n鈮�0,-(n)2 is non-positive.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expression125.

For the function g(x)=4-4x4, find

(a)g(1)

(b)g(-3)

Explain the difference of finding the nthroot of a number when the index is even compared to when the index is odd.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.