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### Simplifying Radical Expressions

A

*radical expression*contains a square root. The expression inside the square root is called a*radicand*.To simplify a radical expression, extract all perfect squares from the radicand.

Use the product and quotient properties of square roots to help you simplify radical expressions.

If the exponent of the variable inside the radical is even and the resulting simplified expression has an odd exponent, take the

*absolute value*of the expression for the simplified expression to guarantee that it is nonnegative.In simplified form, there can be no radicals in the denominator. Removing such radicals is called

*rationalizing*the denominator.To rationalize a

*monomial*denominator, simply multiply the numerator and denominator by the radical in the denominator.To rationalize a

*binomial*denominator, multiply the numerator and denominator by the conjugate of the denominator. The*conjugate*is the same as the original binomial but with the sign between the first term and the second term reversed.To be in

*simplified form*, there must be no perfect squares or fractions in the radicand and there must be no radicals in the denominator.

### Simplifying Radical Expressions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Radical Expressions 0:14
- Radicand
- Example
- Simplest Form
- Example
- Product Property 2:34
- Verifications
- Square Roots of Variables with Even Powers 4:27
- Quotient Rule 6:45
- Example
- Rationalizing Denominators 7:32
- Example
- Conjugates 10:44
- Examples
- Simplest Radical Form 14:44
- Example
- Lecture Example 1 17:34
- Lecture Example 2 19:38
- Additional Example 3
- Additional Example 4

0 answers

Post by Diane Dobmeier on April 17, 2012

Could you please explain to me how cube roots work? I'm trying to do my homework, and I am getting stuck on problems such as, "Reduce the cubic root of 16m to the 5th, n to the 6th. I understand how to do square roots and cube roots with numbers, but the letters throw me off. I tried watching your video, but it didn't address what I needed. Thank you.

0 answers

Post by james gordon on June 6, 2011

Great lecture!

0 answers

Post by Sam McComb on April 1, 2011

Great lesson

0 answers

Post by Mark Mccraney on December 14, 2009

7:00, square root 32 is DIVIDED, not multiplied, by square root 8