Answer Key Simplifying Radicals worksheet
1) 2√108
= 2(√36 * 3)
= 2√36 * √3
= 2(6) * √3
= 12 * √3
= 12√3
11) 2√80 * 4√125
= 2(√16 * 5) * 4(√25 * 5)
= 2√16 * √5 * 4√25 * √5
= 2(4) * √5 * 4(5) * √5
= 8 * √5 * 20 * √5
= 8(20) * (√5 * 5)
= 8(20) * √25
= 160 * 5
= 800
2) 15√2 / √5
= (15√2 * √5) / (√5 * √5)
= (15(√2 * 5)) / ((√5 * 5))
= 15√10 / √25
= 15√10 / 5
= 3√10
12) 4√12 - 5√12
= 4(√4 * 3) - 5(√4 * 3)
= 4√4 * √3 - 5√4 * √3
= 4(2) * √3 - 5(2) * √3
= 8 * √3 - 10 * √3
= 8√3 - 10√3
= (8 - 10)√3
= -2√3
3) 2√27
= 2(√9 * 3)
= 2√9 * √3
= 2(3) * √3
= 6 * √3
= 6√3
13) 9√27 - 5√48
= 9(√9 * 3) - 5(√16 * 3)
= 9√9 * √3 - 5√16 * √3
= 9(3) * √3 - 5(4) * √3
= 27 * √3 - 20 * √3
= 27√3 - 20√3
= (27 - 20)√3
= 7√3
4) 54√2 / √9
= 54√2 / 3
= 18√2
14) 6√27 - 5√12
= 6(√9 * 3) - 5(√4 * 3)
= 6√9 * √3 - 5√4 * √3
= 6(3) * √3 - 5(2) * √3
= 18 * √3 - 10 * √3
= 18√3 - 10√3
= (18 - 10)√3
= 8√3
5) 4√48 * 5√48
= 4 * 5 * (√48 * 48)
= 4 * 5 * √2304
= 4 * 5 * 48
= 960
15) 3√48
= 3(√16 * 3)
= 3√16 * √3
= 3(4) * √3
= 12 * √3
= 12√3
6) 3√50 + 3√18
= 3(√25 * 2) + 3(√9 * 2)
= 3√25 * √2 + 3√9 * √2
= 3(5) * √2 + 3(3) * √2
= 15 * √2 + 9 * √2
= 15√2 + 9√2
= (15 + 9)√2
= 24√2
16) 2√75 - 4√12
= 2(√25 * 3) - 4(√4 * 3)
= 2√25 * √3 - 4√4 * √3
= 2(5) * √3 - 4(2) * √3
= 10 * √3 - 8 * √3
= 10√3 - 8√3
= (10 - 8)√3
= 2√3
7) 27√4 / √9
= 27(2) / 3
= 54 / 3
= 18
17) 5√48
= 5(√16 * 3)
= 5√16 * √3
= 5(4) * √3
= 20 * √3
= 20√3
8) 16√18 - 3√50
= 16(√9 * 2) - 3(√25 * 2)
= 16√9 * √2 - 3√25 * √2
= 16(3) * √2 - 3(5) * √2
= 48 * √2 - 15 * √2
= 48√2 - 15√2
= (48 - 15)√2
= 33√2
18) 4√108 * 5√12
= 4(√36 * 3) * 5(√4 * 3)
= 4√36 * √3 * 5√4 * √3
= 4(6) * √3 * 5(2) * √3
= 24 * √3 * 10 * √3
= 24(10) * (√3 * 3)
= 24(10) * √9
= 240 * 3
= 720
9) 15√48 - 3√48
= 15(√16 * 3) - 3(√16 * 3)
= 15√16 * √3 - 3√16 * √3
19) 7√50 - 4√8
= 7(√25 * 2) - 4(√4 * 2)
= 7√25 * √2 - 4√4 * √2
= 15(4) * √3 - 3(4) * √3
= 60 * √3 - 12 * √3
= 60√3 - 12√3
= (60 - 12)√3
= 48√3
10) 4√20
= 4(√4 * 5)
= 4√4 * √5
= 4(2) * √5
= 8 * √5
= 8√5
= 7(5) * √2 - 4(2) * √2
= 35 * √2 - 8 * √2
= 35√2 - 8√2
= (35 - 8)√2
= 27√2
20) 2√12 * 3√12
= 2 * 3 * (√12 * 12)
= 2 * 3 * √144
= 2 * 3 * 12
= 72