Geometry – Radical Packet
Worksheet 1
Name: ______________________
Simplifying Radicals: The radicand must have no factor that is a perfect square other than 1.
1.
45
5. 2 12
9.
1
175
2
2.
98
3. 162
1
27
3
6. 3 80
7.
10.
11.
99
72
13. 2 63
14. 9 32
15.
1
32
4
17.
40
18. 108
19.
300
21.
1
20
2
25. 10 60
22.
1
48
4
26. 160
4. 5 8
8.
1
18
3
12. 175
16.
2
90
5
20. 4 28
23. 1000
24.
4
150
5
27. 3 1800
28.
3
54
7
Geometry – Radical Packet
Worksheet 2
Name: ______________________
Multiplying Radicals: Answer should be simplified whenever possible.
1.
8⋅ 2
2.
6⋅ 2
3. 5 5 ⋅ 6 2
4. 8 12 ⋅ 6
8. 3 15 ⋅
5. 12 ⋅ 8
6. 10 ⋅ 5
7. 4 10 ⋅ 5 6
9. 5 6 ⋅ 4 8
10. 2 50 ⋅ 3 2
11.
13. 19 ⋅ 19
14.
(
17. 9 8
21.
( 5)
(
)
2
18.
3
26. 4 3
22.
) (2 5 )
2
2
( 6)
4
( 8)
2
5⋅ 6⋅ 2
(
15. 2 5
27 ⋅ 3
)
12.
2
27. 10 10 ⋅ 8 6
6⋅ 6
16. 3 5 ⋅ 4 5
19. 8 11 ⋅11 8
24. 5 3 ⋅ 6 3
2
6
3
(
20. 3 3
25. 10 2 ⋅ 2 3 ⋅ 2 6
)
2
Geometry – Radical Packet
Worksheet 3
Name: ______________________
Simplifying Radicals: No radicals may be left in the denominator of a fraction. This process is called
rationalizing the denominator.
1.
5
2
2.
4
2
3.
12
18
4.
5.
3
5
6.
6
3
7.
8
8
8.
7
3
9.
12
3 2
10.
7
2
11.
3
5
12.
15
5
14.
40
2 20
15.
10 2
5
16.
2
7
13.
4
12
6
2 3
17.
14
7
18.
25
50
19.
18 2
4 12
20.
14 3
4 8
21.
10 10
2 5
22.
7 6
6 6
24.
9
3
25.
5
3 10
Geometry – Radical Packet
Worksheet 4
Name: ______________________
Simplifying Radicals: No radicals may be left in the denominator of a fraction. This process is called
rationalizing the denominator.
1.
3
4
2.
2
3
3.
8
7
4.
7
18
1
3
7.
5
7
8.
12
5
5. 8
7
16
6.
9. 3
5
12
10. 10
1
5
14. 6
11
2
13. 3
1
6
17. 9
4
3
⎛ 5⎞⎛
2 ⎞
20. ⎜ 9 ⎟ ⎜ 6
⎟
⎝ 2 ⎠ ⎝ 15 ⎠
18. 10
11. 5
15.
7
12
3
5
2 4
3 3
12. 8
16.
⎛ 1⎞⎛ 2⎞
19. ⎜ 2 ⎟ ⎜ 3 ⎟
⎝ 6⎠ ⎝ 3⎠
9
2
3 3
5 5
Geometry – Radical Packet
Worksheet 5
Name: ______________________
Dividing Radicals: Roots may be divided only by other roots. Rational numbers may be divided only
by other rational number…remember NO RADICAL in the denominator.
1.
50
2
2.
24
3
3.
10 3
5 3
4.
15 150
5 2
5.
2 24
4 3
6.
54
2
7.
8 18
2 2
8.
15 72
2 6
9.
6 45
3 2
10.
8 60
4 5
11.
13.
15
3 4
16.
5 6 ⋅8 2
2 3⋅4 8
14.
10 10
12 8
6 6
3 12
12.
15.
17.
(10 6 )( 3 5 )
( 2 15 )( 3 )
3 108
12
5 28
2 25
Geometry – Radical Packet
Review Worksheet
Name: ______________________
Simplify
1.
90
5.
2
48
7
4
300
3
2. 10 20
3.
6. 2 3 ⋅ 3 3
7. 6 5 ⋅10 6
9.
5⋅ 5⋅ 6
10. 4 12 ⋅
12.
3
2
5⋅
3
5
3
13.
(
8. 8 2
(
3
24
4
11. 2 5
6
2
14.
1
72
2
4.
2 3
5
)
)
2
2
15.
4
5 3
16.
2
10
17.
15
2 5
18.
3 8
6 2
19.
10
11
20.
5 4
2 5
21.
9
25
22.
6 60
2 10
24.
2 7
6 14