Topic: Radical Expressions
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
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 10.3
- 10.3-10.5 contain many important rules and processes. Spend ample time working through these to get them down well!
- Take note of the "disclaimer" below. It effects answers that may have required absolute values in examples after check point 3. Personally I wish texts wouldn't write blanket disclaimers like this but instead include "given x≠0" or "given x>0" with each problem.
