Rationalizing Denominators

Show your work for each problem.

1.
What should you multiply by to rationalize the denominator?
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply by . This gives in the denominator, eliminating the radical.
2.
Rationalize: . Enter your answer in the form as sqrt(a)/b.
Answer: sqrt(2)/2
. This is the exact value of !
3.
What is the conjugate of ?
1. a)
2. b)
3. c)
4. d)
Answer:
The conjugate of is . So the conjugate of is .
4.
Rationalize:
Answer: 2*sqrt(2)
1. What do you multiply by to rationalize? sqrt(2)/sqrt(2)
2. What is ? 4*sqrt(2)
3. What is ? 2
4. Simplify 2*sqrt(2)
5.
Rationalize: . Enter your answer in the form as a*sqrt(b).
Answer: 2*sqrt(3)
6.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Rationalize:
Answer: sqrt(3)/2
1. Simplify first. What is ? 2*sqrt(3)
2. Rewrite the fraction with simplified denominator 3/(2*sqrt(3))
3. Rationalize . What is the result? 3*sqrt(3)/6
4. Simplify the fraction sqrt(3)/2
8.
Rationalize: . Enter as: a - b*sqrt(c) or a + b*sqrt(c).
Answer: -1 + sqrt(3)
9.
What is the rationalized form of ?
1. a)
2. b)
3. c)
4. d)
Answer:
. This equals .
10.
Rationalize:
Answer: 10 + 5*sqrt(3)
1. What is the conjugate of ? 2 + sqrt(3)
2. Multiply the numerator: 10 + 5*sqrt(3)
3. Multiply the denominators: 1
4. What is the final answer? 10 + 5*sqrt(3)
11.
Rationalize: . Enter as: (a*sqrt(b) - c*sqrt(d))/e.
Answer: 2*sqrt(5) - 2*sqrt(2)
12.
Rationalize:
Answer: sqrt(6) + sqrt(3)
1. What is the conjugate? sqrt(6) + sqrt(3)
2. Multiply numerator: 3*sqrt(6) + 3*sqrt(3)
3. Apply difference of squares to denominator: 3
4. Simplify sqrt(6) + sqrt(3)
13.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. Note that is equal to 5, making answers A and D equivalent.
14.
Rationalize:
Answer: 6 - 2*sqrt(7)
1. What is the conjugate of ? 3 - sqrt(7)
2. Multiply the numerator: 12 - 4*sqrt(7)
3. Apply difference of squares to denominator: 2
4. Simplify 6 - 2*sqrt(7)
15.
Rationalize: . Enter as: (a*sqrt(b) + c*sqrt(d))/e.
Answer: (sqrt(15) + sqrt(6))/3
16.
Which expression is in rationalized form?
1. a)
2. b)
3. c)
4. d)
Answer:
Only has a rational denominator (3). The others all have radicals in their denominators.