Domanda del libro di testo
Evaluate each exponential expression in Exercises 1–22.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 1, Problema 12
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number.
Guida verificata passo dopo passo1
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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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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02:20
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
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