Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Algebra III / Intermediate Algebra
Subtopic: Operations I - Simplify & Multiply

Overview

This topic is devoted to simplifying and manipulating radical expressions. The skills we develop here will be useful in solving radical equations and application problems.

Caution: √(4x2-9) is not equal to √(4x2) - √(9). You cannot break up square roots when the radicand is involved in addition or subtraction. But, if the 4x2 and 9 were multiplied together you could take the square root of each. I.e., √(4x2·9) does equal √4x2·√9 = 2x·3 = 6x. (Well, technically 2|x|·3 = 6|x| unless we were given that x≥0.)

Rule: When multiplying radicals that have the same index, you can rewrite them as one big radical with the radicands multiplied together underneath, and then simplify completely.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 10.3.1 Simplify a radical expression
• 10.3.2 Multiply two radical expressions
• 10.3.3 Understand the "caution" above, i.e. when you can split a radical or not

Text Notes

Many texts make a general "disclaimer" stating something like "assume no radicands involve negative quantities raised to even power". This means that the answer to aradical expression won't have any absolute values no matter what. Personally I wish texts wouldn't write blanket disclaimers like this but instead include "given x≠0" or "given x>0" with each problem. Watch how your text handles this!