How Well Do You Understand Radical Expressions and Equations?

Here is a radical expressions and equations test and key.  Before you take the test let’s do a quick review of the basics of radical expressions and equations.

Key concepts to keep in mind about radical expressions and equations:

* a radical expression is any expression that contains a radical; a square root symbol √ is a an example of a radical
* a radical equation is an equation that involves a radical like a square root
* simplifying a radical expression with a number like √80 involves finding perfect square factors of 80; perfect squares are numbers that have integer square roots examples would be 4, 9, 16, 25, 36, 49, 64, etc. So  in our example we could start to simplify √80 by factoring 80 as 16 x 5 then rewrite √80 as √16 x √5 = 4√5.  This is only one basic example you really need to practice to master simplifying radicals- just focus on those perfect square factors
* we never leave a radical in the denominator of a fraction- we must “rationalize” to rewrite the expression with no radical in the denominator
* to solve radical equations we square both sides of the equation to get rid of the radical- this step can cause some of answers/solutions to be “extraneous” meaning they are no good. As such you MUST verify all solutions to radical equations
* the distance formula is one example where radical equations are needed



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