ISE Intermediate Algebra
ISE Intermediate Algebra
6th Edition
ISBN: 9781264418756
Author: Miller, Julie, O'Neill, Molly, Hyde, Nancy
Publisher: McGraw Hill
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Chapter 6, Problem 1RE
To determine

Whether the answer is true or false.

Expert Solution
Check Mark

Answer to Problem 1RE

Solution:

True

Explanation of Solution

Every positive real number a has a single positive nthroot, called the principal nthroot which is written as an.

An nthroot of a number a, where n is usually assumed to be a positive integer, is a number b which when raised to the power n yields b , i.e., if bn=a, then b=(a)1n is the nthroot of a, here n is the degree of the root.

Any non-zero number complex number has n distinct complex roots of degree n with real roots also.

If n is even and a > 0 where aR, then one of its nthroot is positive, one is negative and the rest are n a considered as complex number has n different “complex roots of degree n, including those with zero imaginary part, i.e., any real roots.

If n is even and a > 0 where aR, one of its nthroot is positive, one is negative and the rest are complex root but not real.

If n is even and a < 0 where aR, none of its nthroot is real.

If n is odd and a > 0 where aR, one of its nthroot is real and has the same sign as a, while the other (n - 1) roots are not real.

Finally if a is not real, then none of its nthroot is real.

Given:

The principal nthroot of an odd-indexed root is always positive.

Conclusion:

The given statement is true.

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Chapter 6 Solutions

ISE Intermediate Algebra

Ch. 6.1 - Prob. 11PECh. 6.1 - Prob. 12PECh. 6.1 - Prob. 13PECh. 6.1 - Prob. 14PECh. 6.1 - Prob. 15PECh. 6.1 - Prob. 16PECh. 6.1 - Prob. 17PECh. 6.1 - Prob. 18PECh. 6.1 - Prob. 19PECh. 6.1 - Prob. 20PECh. 6.1 - For Exercise 21-38, evaluate the roots without...Ch. 6.1 - Prob. 22PECh. 6.1 - Prob. 23PECh. 6.1 - Prob. 24PECh. 6.1 - Prob. 25PECh. 6.1 - Prob. 26PECh. 6.1 - Prob. 27PECh. 6.1 - Prob. 28PECh. 6.1 - Prob. 29PECh. 6.1 - Prob. 30PECh. 6.1 - Prob. 31PECh. 6.1 - Prob. 32PECh. 6.1 - Prob. 33PECh. 6.1 - Prob. 34PECh. 6.1 - Prob. 35PECh. 6.1 - Prob. 36PECh. 6.1 - Prob. 37PECh. 6.1 - Prob. 38PECh. 6.1 - Prob. 39PECh. 6.1 - Prob. 40PECh. 6.1 - Prob. 41PECh. 6.1 - Prob. 42PECh. 6.1 - Prob. 43PECh. 6.1 - For exercise 39-58, simplify the radical...Ch. 6.1 - Prob. 45PECh. 6.1 - Prob. 46PECh. 6.1 - Prob. 47PECh. 6.1 - Prob. 48PECh. 6.1 - Prob. 49PECh. 6.1 - For exercise 39-58, simplify the radical...Ch. 6.1 - Prob. 51PECh. 6.1 - For exercise 39-58, simplify the radical...Ch. 6.1 - Prob. 53PECh. 6.1 - Prob. 54PECh. 6.1 - Prob. 55PECh. 6.1 - Prob. 56PECh. 6.1 - Prob. 57PECh. 6.1 - Prob. 58PECh. 6.1 - Prob. 59PECh. 6.1 - Prob. 60PECh. 6.1 - Prob. 61PECh. 6.1 - Prob. 62PECh. 6.1 - Prob. 63PECh. 6.1 - Prob. 64PECh. 6.1 - Prob. 65PECh. 6.1 - Prob. 66PECh. 6.1 - Prob. 67PECh. 6.1 - Prob. 68PECh. 6.1 - Prob. 69PECh. 6.1 - Prob. 70PECh. 6.1 - Prob. 71PECh. 6.1 - Prob. 72PECh. 6.1 - Prob. 73PECh. 6.1 - Prob. 74PECh. 6.1 - Prob. 75PECh. 6.1 - Prob. 76PECh. 6.1 - Prob. 77PECh. 6.1 - Prob. 78PECh. 6.1 - Prob. 79PECh. 6.1 - Prob. 80PECh. 6.1 - Prob. 81PECh. 6.1 - Prob. 82PECh. 6.1 - Prob. 83PECh. 6.1 - Prob. 84PECh. 6.1 - Prob. 85PECh. 6.1 - Prob. 86PECh. 6.1 - Prob. 87PECh. 6.1 - Prob. 88PECh. 6.1 - Prob. 89PECh. 6.1 - Prob. 90PECh. 6.1 - Prob. 91PECh. 6.1 - Prob. 92PECh. 6.1 - Prob. 93PECh. 6.1 - Prob. 94PECh. 6.1 - Prob. 95PECh. 6.1 - Prob. 96PECh. 6.1 - Prob. 97PECh. 6.1 - Prob. 98PECh. 6.1 - Prob. 99PECh. 6.1 - Prob. 100PECh. 6.1 - Prob. 101PECh. 6.1 - Prob. 102PECh. 6.1 - Prob. 103PECh. 6.1 - Prob. 104PECh. 6.1 - Prob. 105PECh. 6.1 - Prob. 106PECh. 6.1 - Prob. 107PECh. 6.1 - Prob. 108PECh. 6.1 - For Exercise 109-116, use a calculator to evaluate...Ch. 6.1 - Prob. 110PECh. 6.1 - Prob. 111PECh. 6.1 - Prob. 112PECh. 6.1 - For Exercise 109-116, use a calculator to evaluate...Ch. 6.1 - Prob. 114PECh. 6.1 - Prob. 115PECh. 6.1 - For Exercise 109-116, use a calculator to evaluate...Ch. 6.1 - Prob. 117PECh. 6.1 - Prob. 118PECh. 6.1 - 117. Graph Use the graph to confirm the domain...Ch. 6.1 - Prob. 120PECh. 6.2 - Prob. 7PECh. 6.2 - Prob. 8PECh. 6.2 - Prob. 9PECh. 6.2 - Prob. 10PECh. 6.2 - Prob. 11PECh. 6.2 - Prob. 12PECh. 6.2 - Prob. 13PECh. 6.2 - Prob. 14PECh. 6.2 - Prob. 15PECh. 6.2 - Prob. 16PECh. 6.2 - Prob. 17PECh. 6.2 - Prob. 18PECh. 6.2 - Explain how to interpret the expression am/n as a...Ch. 6.2 - Prob. 20PECh. 6.2 - For Exercises 21-24, simplify the expression, if...Ch. 6.2 - Prob. 22PECh. 6.2 - For Exercises 21-24, simplify the expression, if...Ch. 6.2 - Prob. 24PECh. 6.2 - Prob. 25PECh. 6.2 - Prob. 26PECh. 6.2 - Prob. 27PECh. 6.2 - Prob. 28PECh. 6.2 - Prob. 29PECh. 6.2 - Prob. 30PECh. 6.2 - Prob. 31PECh. 6.2 - Prob. 32PECh. 6.2 - Prob. 33PECh. 6.2 - Prob. 34PECh. 6.2 - Prob. 35PECh. 6.2 - Prob. 36PECh. 6.2 - Prob. 37PECh. 6.2 - Prob. 38PECh. 6.2 - Prob. 39PECh. 6.2 - Prob. 40PECh. 6.2 - Prob. 41PECh. 6.2 - Prob. 42PECh. 6.2 - Prob. 43PECh. 6.2 - Prob. 44PECh. 6.2 - Prob. 45PECh. 6.2 - Prob. 46PECh. 6.2 - Prob. 47PECh. 6.2 - 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Prob. 45PECh. 6.7 - Prob. 46PECh. 6.7 - Prob. 47PECh. 6.7 - Prob. 48PECh. 6.7 - Prob. 49PECh. 6.7 - Prob. 50PECh. 6.7 - Prob. 51PECh. 6.7 - Prob. 52PECh. 6.7 - Prob. 53PECh. 6.7 - Prob. 54PECh. 6.7 - Prob. 55PECh. 6.7 - Prob. 56PECh. 6.7 - Prob. 57PECh. 6.7 - Prob. 58PECh. 6.7 - Prob. 59PECh. 6.7 - Prob. 60PECh. 6.7 - Prob. 61PECh. 6.7 - Prob. 62PECh. 6.7 - Prob. 63PECh. 6.7 - Prob. 64PECh. 6.7 - Prob. 65PECh. 6.7 - Prob. 66PECh. 6.7 - Prob. 67PECh. 6.7 - Prob. 68PECh. 6.7 - Prob. 69PECh. 6.7 - Prob. 70PECh. 6.7 - Prob. 71PECh. 6.7 - The time T (in second) required for a pendulum to...Ch. 6.7 - The airline cost for x thousand passengers to...Ch. 6.7 - The time td in seconds it takes an object to drop...Ch. 6.7 - The number of hours needed to cook a turkey that...Ch. 6.7 - For Exercise 76-79, use the Pythagorean theorem to...Ch. 6.7 - Prob. 79PECh. 6.7 - Prob. 80PECh. 6.7 - Prob. 81PECh. 6.8 - Prob. 11PECh. 6.8 - Prob. 12PECh. 6.8 - Prob. 13PECh. 6.8 - Prob. 14PECh. 6.8 - Prob. 15PECh. 6.8 - Prob. 16PECh. 6.8 - Prob. 17PECh. 6.8 - Prob. 18PECh. 6.8 - Prob. 19PECh. 6.8 - Prob. 20PECh. 6.8 - Prob. 21PECh. 6.8 - Prob. 22PECh. 6.8 - Prob. 23PECh. 6.8 - Prob. 24PECh. 6.8 - Prob. 25PECh. 6.8 - Prob. 26PECh. 6.8 - Prob. 27PECh. 6.8 - Prob. 28PECh. 6.8 - Prob. 29PECh. 6.8 - Prob. 30PECh. 6.8 - Prob. 31PECh. 6.8 - Prob. 32PECh. 6.8 - Prob. 33PECh. 6.8 - Prob. 34PECh. 6.8 - Prob. 35PECh. 6.8 - Prob. 36PECh. 6.8 - Prob. 37PECh. 6.8 - Prob. 38PECh. 6.8 - Prob. 39PECh. 6.8 - Prob. 40PECh. 6.8 - Prob. 41PECh. 6.8 - Prob. 42PECh. 6.8 - Prob. 43PECh. 6.8 - Prob. 44PECh. 6.8 - Prob. 45PECh. 6.8 - Prob. 46PECh. 6.8 - Prob. 47PECh. 6.8 - Prob. 48PECh. 6.8 - Prob. 49PECh. 6.8 - Prob. 50PECh. 6.8 - Prob. 51PECh. 6.8 - Prob. 52PECh. 6.8 - Prob. 53PECh. 6.8 - Prob. 54PECh. 6.8 - Prob. 55PECh. 6.8 - Prob. 56PECh. 6.8 - Prob. 57PECh. 6.8 - Prob. 58PECh. 6.8 - Prob. 59PECh. 6.8 - Prob. 60PECh. 6.8 - Prob. 61PECh. 6.8 - Prob. 62PECh. 6.8 - Prob. 63PECh. 6.8 - Prob. 64PECh. 6.8 - Prob. 65PECh. 6.8 - Prob. 66PECh. 6.8 - Prob. 67PECh. 6.8 - Prob. 68PECh. 6.8 - Prob. 69PECh. 6.8 - Prob. 70PECh. 6.8 - Prob. 71PECh. 6.8 - Prob. 72PECh. 6.8 - Prob. 73PECh. 6.8 - Prob. 74PECh. 6.8 - Prob. 75PECh. 6.8 - Prob. 76PECh. 6.8 - Prob. 77PECh. 6.8 - Prob. 78PECh. 6.8 - Prob. 79PECh. 6.8 - Prob. 80PECh. 6.8 - Prob. 81PECh. 6.8 - Prob. 82PECh. 6.8 - Prob. 83PECh. 6.8 - Prob. 84PECh. 6.8 - Prob. 85PECh. 6.8 - Prob. 86PECh. 6.8 - Prob. 87PECh. 6.8 - Prob. 88PECh. 6.8 - Prob. 89PECh. 6.8 - Prob. 90PECh. 6.8 - Prob. 91PECh. 6.8 - Prob. 92PECh. 6.8 - Prob. 93PECh. 6.8 - Prob. 94PECh. 6.8 - Prob. 95PECh. 6.8 - Prob. 96PECh. 6.8 - Prob. 97PECh. 6.8 - Prob. 98PECh. 6.8 - Prob. 99PECh. 6.8 - Prob. 100PECh. 6.8 - Prob. 101PECh. 6.8 - Prob. 102PECh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RECh. 6 - Prob. 69RECh. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 72RECh. 6 - Prob. 73RECh. 6 - Prob. 74RECh. 6 - Prob. 75RECh. 6 - Prob. 76RECh. 6 - Prob. 77RECh. 6 - Prob. 78RECh. 6 - Prob. 79RECh. 6 - Prob. 80RECh. 6 - Prob. 81RECh. 6 - Prob. 82RECh. 6 - Prob. 83RECh. 6 - Prob. 84RECh. 6 - Prob. 85RECh. 6 - Prob. 86RECh. 6 - Prob. 87RECh. 6 - Prob. 88RECh. 6 - Prob. 89RECh. 6 - Prob. 90RECh. 6 - Prob. 91RECh. 6 - Prob. 92RECh. 6 - Prob. 93RECh. 6 - Prob. 94RECh. 6 - Prob. 95RECh. 6 - Prob. 96RECh. 6 - Prob. 97RECh. 6 - Prob. 98RECh. 6 - Prob. 99RECh. 6 - Prob. 100RECh. 6 - Prob. 101RECh. 6 - Prob. 102RECh. 6 - Prob. 1TCh. 6 - Prob. 2TCh. 6 - Prob. 3TCh. 6 - Prob. 4TCh. 6 - Prob. 5TCh. 6 - Prob. 6TCh. 6 - Prob. 7TCh. 6 - Prob. 8TCh. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - Prob. 13TCh. 6 - Prob. 14TCh. 6 - Prob. 15TCh. 6 - Prob. 16TCh. 6 - Prob. 17TCh. 6 - Prob. 18TCh. 6 - Prob. 19TCh. 6 - Prob. 20TCh. 6 - Prob. 21TCh. 6 - Prob. 22TCh. 6 - Prob. 23TCh. 6 - Prob. 24TCh. 6 - Prob. 25TCh. 6 - Prob. 26TCh. 6 - Prob. 27TCh. 6 - Prob. 28TCh. 6 - Prob. 29TCh. 6 - Prob. 30TCh. 6 - Prob. 31TCh. 6 - Prob. 32TCh. 6 - Prob. 33TCh. 6 - Prob. 34TCh. 6 - Prob. 35T
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