Textbook Question
Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 12
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number.
Verified step by step guidance1
Identify the expression inside the square root: \(\sqrt{(-17)^2}\).
Recall that squaring a number means multiplying it by itself, so \((-17)^2 = (-17) \times (-17)\).
Calculate \((-17) \times (-17)\), which results in a positive number because a negative times a negative is positive.
Rewrite the expression as \(\sqrt{\text{positive number}}\).
Since the square root of a positive number is a real number, simplify \(\sqrt{(-17)^2}\) to the absolute value of \(-17\), which is \(17\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Root and Its Properties
The square root of a number is a value that, when multiplied by itself, gives the original number. For non-negative numbers, the square root is real and non-negative. Understanding how to simplify square roots, especially with squared terms, is essential for evaluating expressions like √(−17)^2.
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Imaginary Roots with the Square Root Property
Order of Operations
The order of operations dictates the sequence in which parts of a mathematical expression are evaluated. Parentheses and exponents are handled before roots. In the expression √(−17)^2, the exponent applies to −17 first, then the square root is taken, which affects the final result.
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8:38Performing Row Operations on Matrices
Real Numbers and Imaginary Numbers
Real numbers include all rational and irrational numbers, while imaginary numbers involve the square root of negative values. Recognizing when an expression results in a real number or when it involves imaginary numbers helps determine if the root is real or not, as asked in the question.
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03:31Introduction to Complex Numbers
Related Practice
Textbook Question
Evaluate each exponential expression in Exercises 1–22. 4−3
Textbook Question
In Exercises 11–16, factor by grouping. x3−3x2+4x−12
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Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 5(x+2)/(2x-14), for x=10
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Textbook Question
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (17x3−5x2+4x−3)−(5x3−9x2−8x+11)
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Textbook Question
Express the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.