Simplifying Radicals | Answer Key

University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2021
Views:

131

Pages:

3
Author:

Killian Mata

ALGEBRA 2 TRIG Unit 1 Name:_________________________________ Date:_____________ Radical Sign Vocabulary: Radical – the whole expression x Radicand Let’s list the perfect squares from 1 – 400… Properties of Radicals: Product Property: ab  a  b Quotient Property: a  b a b *A radical expression is considered to be simplified, only if: 1) There are no perfect square factors left under the radical sign. 2) There are no radicals in the denominator.  You must eliminate radicals in the denominator by using a process called rationalizing the denominator. Examples: Simplify the expression. 1) 2)  500 24 4)  4 12 5) 3) 3 27 6  15 6) 3 12  2 6 7) 4 25 8) 7 16 9) 11) 2 11 12) 12 5 13) 25 3 10) 7 2 8 3 14) 20 27 Division of Radicals:  If possible, you can simplify the numbers underneath the radicals BEFORE rationalizing. Examples: Simplify. 6 3 15) 16) 6 10 8 2 17) 18 7 72 14 18) 19) 12 2 2 6 3 8 2 10 Adding/Subtracting Radicals:   You can only add or subtract radicals if the #’s under the radical sign (the radicands) are the same! Add or subtract only the #’s outside of the radicals (the coefficients). Examples: Simplify. 20) 2 36 3 21) 23) 22 7  11 7 24)  10 6  9 6 20  45 22) 5 5 8 6 25)  5 7  63 Multiplying Radicals:  Distribute or FOIL where necessary and apply the Product Property. Examples: Simplify. 26)  5 6 3  29)  5  3  5  3   27) 2 3 7 4 30) 2  3   28) 9  6 4  6  31) 3  2 2  5  2 Conjugates:    Have the same numbers, but opposite signs in the middle: a + b and a – b a  b and a  b are conjugates.  When multiplied, all of the square roots disappear. Use conjugates to help rationalize the denominator when there are 2 terms in the denominator. Examples: Simplify. 32) 34) 5 3 5 1 3 5 33) 35) 2 5 36) 5 5 3 5 6 2 7 2 3 5 7 37) 3 7