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Algebra 1 Simplifying Radical Expressions

Section 10: Radical Expressions and Equations: Lecture 1 | 41:30 min

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Lecture Comments (26)

	2 answers Last reply by: Juan Collado Fri Dec 29, 2017 12:40 PM Post by asiel nasser on January 28, 2016 where is example 4 answer?????????????????
	1 answer Last reply by: Dr Carleen Eaton Sun Apr 26, 2015 12:33 PM Post by Andria Sperry on April 18, 2015 Can't 6/33 be simplified to 2/11?
	1 answer Last reply by: Dr Carleen Eaton Sat Feb 23, 2013 6:51 PM Post by Rishabh Kasarla on February 21, 2013 At 41:09, why is it 2 instead of 12 in the answer?
	0 answers Post by Victor Castillo on January 27, 2013 I feel stupid now.
	1 answer Last reply by: Dr Carleen Eaton Sun Jan 27, 2013 1:15 PM Post by Victor Castillo on January 27, 2013 What happened to the square root signs?
	0 answers Post by Victor Castillo on January 27, 2013 OMG you lost me here
	0 answers Post by Victor Castillo on January 27, 2013 Please clarify I am so lost.
	1 answer Last reply by: Dr Carleen Eaton Sun Jan 27, 2013 1:14 PM Post by Victor Castillo on January 27, 2013 At 33:55 what decides wether the 3 goes inside or outside in this case of the square root sign?This whole lesson is really messing with my head.
	1 answer Last reply by: Dr Carleen Eaton Sun Jan 27, 2013 1:12 PM Post by Victor Castillo on January 27, 2013 You also added absolute value signs then you removed them.Why add them in the first place?
	1 answer Last reply by: Dr Carleen Eaton Sun Jan 27, 2013 1:09 PM Post by Victor Castillo on January 27, 2013 I am so confused the square root sign disappeared at 30:21 and you say you eliminated the radicals but they are still there.Doesn't X3 contain and Y2 contain a radical?Please clarify.
	1 answer Last reply by: Dr Carleen Eaton Sun Jan 27, 2013 1:07 PM Post by Victor Castillo on January 27, 2013 At 20:42 what happens to the 5?Why does it seem you skip steps or at least explanations constantly.It is frustrating!
	1 answer Last reply by: Dr Carleen Eaton Sun Jan 27, 2013 1:03 PM Post by Victor Castillo on January 27, 2013 Does it have to do with square root?
	0 answers Post by Victor Castillo on January 27, 2013 not itself...
	0 answers Post by Victor Castillo on January 27, 2013 Why divide the exponent by 2 and n ot itself??
	1 answer Last reply by: Dr Carleen Eaton Mon Apr 16, 2012 10:05 PM Post by Diane Dobmeier on April 12, 2012 Could you please explain to me how cubic roots work? I'm trying to do my homework, and I'm stuck on problems like "Reduce", for instance, the cubic root of 16 m to the fifth power, n to the fourth power'. I just watched your video, but I don't understand how to simplify roots when there are letters involved. I understand the numbers part, but the letters are throwing me off. Thanks!

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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

Simplify:
√8 ×√{22}

√{8 ×22}
√{176}
√{4 ×44}
√{4 ×4 ×11}
√{4 ×4} ×√{11}
2 ×2 ×√{11}

4√{11}

Simplify:
√7 ×√{40}

√{12 ×40}
√{280}
√{4 ×70}
√4 ×√{70}

2√{70}

Simplify:
√{12} ×√{40}

√{12 ×40}
√{480}
√{4 ×120}
√{4 ×4 ×30}
√{4 ×4} ×√{30}
2 ×2 ×√{30}

4√{30}

Simplify:
√{14x³y²} ×√{6x²y²}

√{14x³y² ×6x²y²}
√{84x⁵y⁴}
√{4 ×21x⁴xy⁴}
√{4x⁴y⁴} ×√{21x}
2Px²Py²P ×√{21x}

2x²y² ×√{21x}

Simplify:
√{6a²b³c⁴} ×√{20a²b³c}

√{6a²b³c⁴ ×20a²b³c}
√{120a⁴b⁶c⁵}
√{4 ×30a⁴b⁶c⁴c}
√{4a⁴b⁶c⁴} ×√{30c}
2| a² || b³ || c² | ×√{30c}

2a²| b³ |c²√{30c}

Simplify:
√{15g³hi²} ×√{10g²h⁴i³}

√{15g³hi² ×10g²h⁴i³}
√{150g⁵h⁵i⁵}
√{25 ×6g⁴gh⁴hi4i}
√{25g⁴h⁴i⁴} ×√{6ghi}
5| g² || h² || i² | ×√{6ghi}

5g²h²i²√{6ghi}

Simplify:
√{[10/2]}

[(√{10} )/(√2 )] ×[(√2 )/(√2 )]
[(√{10 ×2} )/(( √2 )²)]
[(√{2 ×2 ×5} )/2]

[(2√5 )/2]

Simplify:
√{[24/7]}

[(√{24} )/(√7 )] ×[(√7 )/(√7 )]
[(√{24 ×7} )/(( √7 )²)]
[(√{168} )/7]
[(√{4 ×42} )/7]

[(2√{42} )/7]

Simplify:
[(4√2 )/(2√3 − 5√2 )]

[(4√2 )/(2√3 − 5√2 )] ×[(2√3 + 5√2 )/(2√3 + 5√2 )]
[(8√2 √3 + 20√2 √2 )/(( 2√3 )² − ( 5√2 )²)]
[(8√{2 ×3} + 20( √2 )²)/(( 2√3 )² − ( 5√2 )²)]
[(8√6 + 20 ×2)/(4 ×3 − 25 ×2)]
[(8√6 + 40)/(12 − 50)]

[(8√6 + 40)/( − 38)]

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Answer

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 Expression 0:12

Example: Radicand Simplest Form
Example: Not Simplest Form
Principal Square Root (Positive)

Product Property 3:40

Examples

Square Roots of Variables with Even Powers 7:01

Eliminate Radical Sign
Divide Exponent by 2
Absolute Value of Result
Examples

Quotient Rule 14:12

Example

Rationalizing Denominators 16:08

Example

Conjugates 18:33

Example

Simplest Radical Form 20:58

Three Criteria

Example 1: Simplify Expression 21:57
Example 2: Simplify Expression 25:12
Example 3: Simplify Expression 31:37
Example 4: Simplify Expression 35:29

Algebra 1 Online Course

Section 1: Basic Concepts
	Variables and Expressions	11:22
	Order of Operations	15:59
	Distributive Property	9:50
	Real Number System	17:58
	Functions and Graphs	34:39
Section 2: Solving Linear Equations
	From Sentences to Equations	16:05
	Addition and Subtraction Techniques	15:24
	Multiplication and Division Techniques	15:41
	Techniques for Multistep Equations	14:31
	When the Variable is on Both Sides of the Equation	20:17
	Ratios and Proportion	16:05
	Applications of Percents	13:46
	More Than One Variable	20:38
Section 3: Functions
	Relations	16:58
	Functions	19:27
	Linear Functions	20:15
Section 4: Linear Functions and Their Graphs
	Slope and Rate of Change	19:46
	Direct Variation	13:54
	Slope Intercept Form of an Equation	12:06
	Point Slope Form of an Equation	9:07
	Parallel Lines and Perpendicular Lines	18:02
Section 5: Systems of Equations
	Graphing Systems of Equations	22:45
	Solving by Substituting	22:41
	Solving by Addition and Subtraction	16:13
Section 6: Inequalities
	Addition & Subtraction Techniques	11:34
	Multiplication & Division Techniques	10:49
	Techniques for Multistep Inequalities	16:56
	Compound Inequalities	21:32
	Equations with Absolute Value	24:16
	Inequalities with Absolute Values	17:37
	Graphing Inequalities with Two Variables	24:33
	Graphing Systems of Inequalities	24:04
Section 7: Polynomials
	Multiplying Monomials	22:19
	Dividing Monomials	24:02
	Polynomials	8:56
	Adding and Subtracting Polynomials	15:51
	Multiplying Polynomials by Monomials	18:17
	Multiplying Polynomials	18:02
	Special Products	17:00
Section 8: Factoring
	Special Product	17:51
	Factoring Using Greatest Common Factor	25:21
	Factoring Trinomials with Leading Coefficient of 1	27:11
	Factoring General Trinomials	46:09
	Factoring the Difference of Two Squares	24:03
	Factoring Perfect Squares	18:10
Section 9: Quadratic Functions
	Graphing Quadratic Functions	35:45
	Solving Equations by Graphing	40:42
	Solving Equations by Completing the Square	28:13
	Solving Equations Using the Quadratic Formula	17:17
Section 10: Radical Expressions and Equations
	Simplifying Radical Expressions	41:30
	Operations with Radical Expressions	21:52
	Solving Radical Equations	27:00
	Pythagorean Theorem	17:24
	Distance Formula	26:50
Section 11: Rational Expressions and Equations
	Inverse Variation	24:13
	Rational Expressions	34:22
	Multiplying Rational Expressions	22:58
	Dividing Rational Expressions	21:49
	Dividing Polynomials	35:57
	Adding and Subtracting Rational Expressions with Like Denominators	17:38
	Adding and Subtracting Rational Expressions with Unlike Denominators	37:16
	Complex Fractions	25:38
	Rational Equations	38:09

Related Books

Algebra: Structure and Method, Book 1

Authors: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

ISBN: 395977223

Publisher: McDougal Littell

Year: 2000

This classic textbook does a great job of explaining concepts and includes lots of in-depth, worked out examples in every section.

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Dr. Carleen Eaton

Simplifying Radical Expressions

Slide Duration:

Table of Contents

Section 1: Basic Concepts

Variables and Expressions

11m 22s

Intro