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: √(4x^{2}-9) is not equal to √(4x^{2}) - √(9). You cannot break up square roots when the radicand is involved in addition or subtraction. But, if the 4x^{2} and 9 were *multiplied* together you could take the square root of each. I.e., √(4x^{2}·9) does equal √4x^{2}·√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!