Fol-lowing is a deﬁnition of radicals. 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. Simplifying Radical Expressions 2. A. Simplifying Radical Expressions with Variables . 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 I can simplify radical algebraic expressions. 6!2x 5!3 51. 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. 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 !14 ? Multiplying and Dividing 3. I can use properties of exponents to simplify expressions. More Examples: 1. !3 150 ? A simplified radical expression cannot have a radical in the denominator. !3Q!12 2 !6R 50. 11/4/2020 7.5 Multiplying and Dividing Radical Expressions-judith 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 . Write the product in simplest form. Multiply the factors in the second radicand. Examples: a. ˆ ˙ ˆ ˝ ˚ ˝ ˚ ˝ ˘ c. ˆ 4 Once we multiply the radicals, we then look for factors that are a power of the index and simplify the radical whenever possible. 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. Simplify each expression. Multiplying Radical Expressions. The result is \(12xy\). Factor 24 using a perfect-square factor. Multiplying Radical Expressions When the denominator has a radical in it, we must multiply the entire expression by some form of 1 to eliminate it. To multiply \(4x⋅3y\) we multiply the coefficients together and then the variables. Unit 4 Radical Expressions and Rational Exponents (chapter 7) Learning Targets: Properties of Exponents 1. m a √ = b if bm = a The small letter m inside the radical … Answers to Multiplying Radicals of Index 2: No Variable Factors 1) 6 2) 4 3) Distribute Ex 1: Multiply. 47. All variables represent nonnegative numbers. 8 "3 2x2 52. Rationalize all denominators. ˆ(" ˙ ˚ ˝(˘ ˛ ! II. Multiplying radicals with coefficients is much like multiplying variables with coefficients. 4. View 7.5 Multiplying and Dividing Radical Expressions-judith castaneda.pdf from MAT 115 at California Baptist University. Product Property of Square Roots Simplify. 3 20 49. I can multiply radical expressions. Assume that all variables are positive. ˘ ˚ 4 ˙ " 4 b. 21 48. 30a34 a 34 30 a17 30 2. Objective: Simplify radicals with an index greater than two. Elementary Algebra Skill Multiplying Radicals of Index 2: No Variable Factors. Rationalize the denominator: The basic steps follow.