Dividing Radicals

Show your work for each problem.

1.
Simplify
1. a)
2. b)
3. c)
4. d)
Answer:
2.
Simplify
Answer: 2
3.
Simplify step by step.
Answer: 3
1. Apply the quotient rule. What is ? sqrt(9)
2. What is ? 3
4.
Simplify
1. a)
2. b)
3. c)
4. d)
Answer:
5.
Simplify
Answer: 3
6.
Simplify step by step.
Answer: 4
1. Apply the quotient rule. What is ? 16
2. What is ? 4
7.
Simplify
1. a)
2. b)
3. c)
4. d)
Answer:
. Note: and are the same!
8.
Simplify
Answer: 7
9.
Simplify step by step.
Answer: 5
1. What is ? 25
2. What is ? 5
10.
Rationalize the denominator:
1. a)
2. b)
3. c)
4. d)
Answer:
11.
Rationalize:
Answer: 2sqrt(3)
1. Multiply numerator and denominator by . What is the new numerator? 6sqrt(3)
2. What is the new denominator? ? 3
3. Simplify 2sqrt(3)
12.
Simplify
Answer: 2sqrt(3)
13.
Simplify
1. a)
2. b)
3. c)
4. d)
Answer:
. Note: is not fully simplified!
14.
Rationalize:
Answer: 2sqrt(5)
1. Multiply by . What is the new numerator? 10sqrt(5)
2. What is the new denominator? 5
3. Simplify 2sqrt(5)
15.
Simplify
Answer: 3sqrt(3)
16.
Rationalize the denominator:
Answer: -3 + 3sqrt(2)
1. What is the conjugate of ? 1 - sqrt(2)
2. What is ? -1
3. The answer is . Simplify. -3 + 3sqrt(2)
17.
Rationalize:
1. a)
2. b)
3. c)
4. d)
Answer:
18.
Simplify completely:
Answer: 8
1. Apply the quotient rule. What is ? 64
2. What is ? 8