Rewriting Radical Expressions with Rational Exponents

(Video) Square Roots with Variables

by Eric Buffington

Eric Buffington has a great video on Simplifying Radicals with variables in them.

(Video) Simplifying Square Roots and Cube Roots with Variables

by OrlandoHSMath

Here is a good video from OrlandoHSMath about simplifying radicals, square roots and cube roots.

Radical expressions with exponents are not that difficult to deal with.

Since radicals can also be expressed as exponents, the easiest way to deal with them is to switch all the radicals to exponents and then apply our rules of exponents. The way you do this is as follows: $$\sqrt[n]x\;\;\rightarrow\;\;x^{1/n}$$ If you apply this to an exponent within a radical, using our rules of exponents, we would just multiply the exponents together! It would look something like this: $$\sqrt[n]{x^m}\;\;\rightarrow\;\;x^{m/n}$$ See! Very easy! Remember, If there is no number assigned to a radical, it is always a square root. That means the implied number is 2, so you simply divide the exponent in half.