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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.

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