Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

1:36 minutes

Problem 51a

Textbook Question

In Exercises 47–54, find each cube root. _____ ³√1/125

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Key Concepts

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

Cube Roots

A cube root of a number 'x' is a value 'y' such that y³ = x. This means that when 'y' is multiplied by itself three times, it equals 'x'. For example, the cube root of 8 is 2, since 2³ = 8. Understanding cube roots is essential for solving problems involving cubic equations or expressions.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In the case of 1/125, both 1 and 125 are integers, making it a rational number. Recognizing rational numbers is important when dealing with roots, as they can often simplify calculations.

Properties of Exponents

The properties of exponents govern how to manipulate expressions involving powers. For cube roots, the property states that (a/b)^(1/3) = a^(1/3) / b^(1/3). This property allows us to separate the numerator and denominator when finding roots, making it easier to compute the cube root of fractions like 1/125.