Textbook Question
Simplify by reducing the index of the radical :
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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 72
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -26 and -3
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Identify the two numbers given: -26 and -3.
Recall that the distance between two numbers \(a\) and \(b\) on the number line can be expressed as the absolute value of their difference: \(\left| a - b \right|\).
Write the distance between -26 and -3 as \(\left| -26 - (-3) \right|\).
Simplify the expression inside the absolute value: \( -26 - (-3) = -26 + 3 \).
Evaluate the absolute value expression \(\left| -26 + 3 \right|\) to find the distance.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative. For example, |−3| = 3 and |3| = 3, showing that both are three units away from zero.
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Distance Between Two Numbers
The distance between two numbers on the number line is the absolute value of their difference. This means the distance between numbers a and b is |a − b|, which ensures the result is non-negative and represents the length between the points.
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Evaluating Absolute Value Expressions
To find the distance, first write the absolute value expression representing the difference between the two numbers. Then subtract the numbers inside the absolute value and simplify. Finally, take the absolute value to get the positive distance.
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Related Practice
Textbook Question
In Exercises 65–92, factor completely, or state that the polynomial is prime. x3+2x2−9x−18
Textbook Question
Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree.
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Textbook Question
Simplify the radical expressions in Exercises 67–74, if possible. ⁵√64x6/⁵√2x
Textbook Question
In Exercises 67–82, find each product. (7x2 y+1)(2x2 y−3)
Textbook Question
In Exercises 69–82, simplify each complex rational expression. (1/x + 1/y)/(x+y)