Simplifying Radical Expressions with Variables

When radicals (square roots) include variables, they are still simplified the same way. We just have to work with variables as well as numbers

1) Factor the radicand (the numbers/variables inside the square root). Factor the number into its prime factors and expand the variable(s).
2) Bring any factor listed twice in the radicand to the outside.


Examples:

1)
Since there was a pair of 3's and a pair of y's, we brought the 3 and the y outside, but the x stayed inside since it was not a pair.


2)

3)
Notice that there were two pairs of x's, so we were able to bring two to the outside. The last x, however, was not part of a pair and thus stayed inside.


Practice: Simplify

1)

2)

3)

4)

5)


Answers: 1)2)3)4)5)

Related Links:
Math
Algebra
Factors


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