Multiplying Radicals

Show your work for each problem.

1.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. We multiply the radicands (2 and 3) and keep the result under one radical.
2.
Simplify:
Answer: 5
. The square root and squaring are inverse operations.
3.
Calculate:
Answer: 6
. Alternatively: .
4.
What is simplified?
1. a)
2. b)
3. c)
4. d)
Answer:
. Always simplify your final answer!
5.
Multiply and simplify:
Answer: 6
1. Multiply the radicands: 36
2. So 36
3. What is ? 6
6.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Simplify:
Answer: 18
8.
Multiply and simplify:
Answer: 4sqrt(3)
1. Multiply the radicands: 48
2. Find the largest perfect square factor of 48 16
3. What is ? 4
4. So the simplified answer is 3
9.
Multiply:
Answer: 30sqrt(3)
1. Multiply the coefficients: 15
2. Multiply the radicands: 12
3. Factor 12: What is the largest perfect square factor? 4
4. 2
5. Final answer: 30
10.
What is the coefficient in when simplified?
Answer: 10
. The result is a whole number (coefficient 10 with no remaining radical).
11.
Which expression equals ?
1. a)
2. b)
3. c)
4. d)
Answer:
12.
Simplify:
Answer: 20
1. What is ? 4
2. What is ? 5
3. Multiply: 20
13.
Simplify and give the coefficient.
Answer: 40
. The coefficient is 40.
14.
Multiply and simplify:
Answer: 24sqrt(3)
1. Multiply the coefficients: 6
2. Multiply the radicands: 48
3. What is the largest perfect square factor of 48? 16
4. 4
5. Final coefficient: 24
15.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
16.
Simplify:
Answer: 12
1. Multiply the radicands: 144
2. Is 144 a perfect square? yes
3. What is ? 12
17.
If and , what is ?
Answer: 24
. If , then , so .
18.
Simplify:
Answer: 60
1. Multiply the coefficients: 15
2. Multiply the radicands: 16
3. What is ? 4
4. Final answer: 60