Adding and Subtracting Radicals

Show your work for each problem.

1.
Which expression shows like radicals?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
and are like radicals because both have (same radicand). The other pairs have different radicands.
2.
Simplify:
Answer: 7*sqrt(3)
. Just add the coefficients and keep the radical.
3.
Simplify:
Answer: 5*sqrt(7)
. Just subtract the coefficients and keep the radical.
4.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. Don't forget the implicit coefficient of 1!
5.
Simplify:
Answer: 5*sqrt(2)
1. Are all terms like radicals? yes
2. Combine the coefficients: 6 + 3 - 4 = ? 5
3. What is the final answer? 5*sqrt(2)
6.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. So .
7.
Simplify:
Answer: 5*sqrt(5)
1. Simplify . What is it equal to? 2*sqrt(5)
2. Simplify . What is it equal to? 3*sqrt(5)
3. Now add the like radicals: 5*sqrt(5)
8.
Simplify:
Answer: 2*sqrt(3)
and . So .
9.
Which expression cannot be simplified further?
1. a)
2. b)
3. c)
4. d)
Answer:
has different radicands (3 and 7, both prime) so they cannot be combined. The others can all be simplified: , , .
10.
Simplify:
Answer: 4*sqrt(2)
1. Simplify 5*sqrt(2)
2. Simplify 2*sqrt(2)
3. Simplify 3*sqrt(2)
4. Combine: 4*sqrt(2)
11.
Simplify:
Answer: 4*sqrt(5) - 2*sqrt(3)
Group like radicals: .
12.
Simplify:
Answer: 9*sqrt(2)
1. Simplify 6*sqrt(2)
2. Simplify 4*sqrt(2)
3. Simplify 7*sqrt(2)
4. Combine: 9*sqrt(2)
13.
A triangle has sides m, m, and m. What is its perimeter?
1. a) m
2. b) m
3. c) m
4. d) m
Answer: m
, , . Perimeter = m.
14.
Simplify:
Answer: 8*sqrt(7)
, , . So .
15.
Simplify:
Answer: 8*sqrt(5)
1. Simplify 5*sqrt(5)
2. Simplify 4*sqrt(5)
3. Simplify 3*sqrt(5)
4. Simplify 2*sqrt(5)
5. Combine: 8*sqrt(5)
16.
Simplify:
Answer: sqrt(6)
1. Simplify 3*sqrt(6)
2. Simplify 2*sqrt(6)
3. Simplify 4*sqrt(6)
4. Combine: sqrt(6)