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

1:39 minutes

Problem 33c

Textbook Question

In Exercises 33–46, simplify each expression. __ √5²

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Key Concepts

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

Square Roots

A square root of a number 'x' is a value 'y' such that y² = x. In this context, the square root symbol (√) indicates that we are looking for a number that, when multiplied by itself, gives the original number. For example, √25 = 5 because 5² = 25.

Properties of Exponents

The properties of exponents govern how to manipulate expressions involving powers. One key property is that (a^m)² = a^(2m), which means squaring a number raised to a power doubles the exponent. This is essential for simplifying expressions like √(a²) = a, where 'a' is a non-negative number.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form. This can include combining like terms, applying the distributive property, and using square roots and exponents. In the case of √5², simplification leads to the result of 5, as the square root and the square cancel each other out.