In this lesson, we are only going to deal with square roots only which is a specific type of radical expression with an index of \color{red}2.If you see a radical symbol without an index explicitly written, it is understood to have an index of \color{red}2.. Below are the basic rules in multiplying radical expressions. !3 150 ? 30a34 a 34 30 a17 30 2. Write the product in simplest form. 8 "3 2x2 52. Multiply the factors in the second radicand. A simplified radical expression cannot have a radical in the denominator. Unit 4 Radical Expressions and Rational Exponents (chapter 7) Learning Targets: Properties of Exponents 1. View 7.5 Multiplying and Dividing Radical Expressions-judith castaneda.pdf from MAT 115 at California Baptist University. Simplify radical expressions Rationalize denominators (monomial and binomial) of radical expressions Add, subtract, and multiply radical expressions with and without variables Solve equations containing radicals 3 20 49. Product Property of Square Roots Simplify. Multiplying Radical Expressions m a √ = b if bm = a The small letter m inside the radical … Objective: Simplify radicals with an index greater than two. Answers to Multiplying Radical Expressions of Index 2: With Variable Factors 1) −12 x3 3 2) −60n 2n 3) −8x 15x 4) 45n 3n 5) −36x2 10x 6) −90n2 7) 20x 15 8) 6m m 9) −20 2b − 12 5b 10) 10x + 25x 11) 12k 3 − 6 2k 12) −15n 10 + 50 When the denominator has a radical in it, we must multiply the entire expression by some form of 1 to eliminate it. II. 4. The result is \(12xy\). A. !3Q!12 2 !6R 50. Rationalize all denominators. To multiply \(4x⋅3y\) we multiply the coefficients together and then the variables. 21 48. Simplify each expression. Assume that all variables are positive. The basic steps follow. 6!2x 5!3 51. Factor 24 using a perfect-square factor. More Examples: 1. I can multiply radical expressions. Simplifying Radical Expressions 2. All variables represent nonnegative numbers. Once we multiply the radicals, we then look for factors that are a power of the index and simplify the radical whenever possible. ˆ ˙ ˆ ˝ ˚ ˝ ˚ ˝ ˘ c. ˆ 4 Multiplying and Dividing 3. While square roots are the most common type of radical we work with, we can take higher roots of numbers as well: cube roots, fourth roots, fifth roots, etc. MULTIPLICATION OF RADICALS: To multiply radicals, just multiply using the same rules as multiplying polynomials (Distributive Property, FOIL, and Exponent Rules) except NEVER multiply values outside the radical times values inside the radical. Rationalize the denominator: 11/4/2020 7.5 Multiplying and Dividing Radical Expressions-judith !14 ? Examples: a. Elementary Algebra Skill Multiplying Radicals of Index 2: No Variable Factors. 47. Distribute Ex 1: Multiply. I can use properties of exponents to simplify expressions. Simplifying Radical Expressions with Variables . ˘ ˚ 4 ˙ " 4 b. Simplifying simple radical expressions Ex 1: Ex 2: 80 50 125 450 = = = = 16*5 25* 2 25*5 225* 2 = = = = 4 5 52 5 5 ... -multiply any numbers in front of the radical; multiply any numbers inside of the radical . Answers to Multiplying Radicals of Index 2: No Variable Factors 1) 6 2) 4 3) ˆ(" ˙ ˚ ˝(˘ ˛ ! Fol-lowing is a definition of radicals. I can simplify radical algebraic expressions. Multiplying Radical Expressions. Multiplying radicals with coefficients is much like multiplying variables with coefficients.