Simplifying Square Roots of Powers in Radical Expressions

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  • 0:02 Find a Partner
  • 0:27 What Do Those Radical…
  • 0:56 Radicals With Exponents
  • 2:52 Reducing Radicals…
  • 3:21 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

Simplifying radical expressions that contain powers can be tricky. There are a few simple rules that will help you perform these simplifications with ease. This lesson will teach you how.

Find a Partner

There are many instances where finding a partner can be a necessity. Dancing can be better with a partner. So can riding amusement park rides. You can be someone's 'partner in crime' or just say to them 'Howdy Pardner!'

Your partner is someone who will watch out for you and warn you of possible problems on the road ahead. This lesson will explain the importance of partners in simplifying radical expressions containing exponents. It really is the most important part.

What Do Those Radical Symbols Mean?

The radical symbol looks like this:


and is defined as a number that gives a specified quantity when multiplied to itself. For example, the square root of 25 is 5. 5 is a number that when multiplied to itself gives the specific number 25. This also means that the inverse of the square root is squared. When you square a number, taking its square root brings you back to the original number. The square root of 16 = 4; 4^2 = 16.

Radicals with Exponents

Since the radical symbol is the opposite of squared, we can make the following statement: the square root of x^2 = x.

This just means that the square root of any term squared is equal to that term. So the square root of 4^2 is 4, the square root of b^2 is b, and so on. We can use this general rule to solve problems like this - Simplify: x^5 * y^2.

The first step to solving this problem is to write each of the exponential terms out the long way. Then we match every term up with a partner. In these problems, the partners have to be the same term - no matching x's with y's.

Now, since we know that the square root of x^2 is x, we can simplify this expression. Every term that is a squared term under the radical symbol can be simplified to a single term outside the radical symbol.

So every x^2 under the radical will simplify to an x outside the radical, and every y with a partner will simplify to a single y outside of the square root symbol. If there is a term without a partner, it will stay under the radical.

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