Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:14 minutes

Problem 9

Textbook Question

In Exercises 1–12, find each absolute value.|-√2|

Verified step by step guidance

Understand that the absolute value of a number is its distance from zero on the number line, regardless of direction.

Recognize that the absolute value of a number is always non-negative.

Identify the expression inside the absolute value: \(-\sqrt{2}\).

Since \(-\sqrt{2}\) is a negative number, the absolute value will be the positive version of it.

Therefore, the absolute value of \(-\sqrt{2}\) is \(\sqrt{2}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by two vertical bars surrounding the number or expression, such as |x|. For any real number x, the absolute value is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0.

Square Root

The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as √x. For positive numbers, there are two square roots: one positive and one negative. However, the principal square root is the non-negative one, which is typically what is referred to when using the square root symbol.

Negative Numbers

Negative numbers are values less than zero and are represented on the left side of zero on the number line. When calculating the absolute value of a negative number or expression, the result is always positive. For example, |-√2| involves finding the absolute value of a negative square root, which will yield a positive result.