12. ANSWER: 6
10-4 Radical Equations
Solve each equation. Check your solution.
14. ANSWER: 11
2. ANSWER: 40
16. ANSWER: 3
4. ANSWER: 4
18. ANSWER: 0
6. ANSWER: 3
8. EXERCISE Suppose the function
20. ,
where S represents speed in meters per second and
is the leg length of a person in meters, can
approximate the maximum speed that a person can
run.
a. What is the maximum running speed of a person
with a leg length of 1.1 meters to the nearest tenth of
a meter?
b. What is the leg length of a person with a running
speed of 6.7 meters per second to the nearest tenth
of a meter?
c. As leg length increases, does maximum speed
increase or decrease? Explain.
ANSWER: a. 8.2 m/s
b. 0.7 m
c. Increases; sample answer: As the leg length
increases, the value of the radicand also increases.
Solve each equation. Check your solution.
10. ANSWER: 121
ANSWER: 47
Solve each equation. Check your solution.
22. ANSWER: no solution
24. ANSWER: 26. ANSWER: 11
28. CCSS REASONING The formula for the slant
height c of a cone is
, where h is the
height of the cone and r is the radius of its base. Find
the height of the cone if the slant height is 4 and the
radius is 2. Round to the nearest tenth.
12. ANSWER: 6
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ANSWER: 11
ANSWER: or ≈ 3.5
Page 1
34. OPEN ENDED Write a radical equation with a
variable on each side. Then solve the equation.
26. ANSWER: 10-4ANSWER: Radical Equations
11
Sample answer:
28. CCSS REASONING The formula for the slant
height c of a cone is
, where h is the
height of the cone and r is the radius of its base. Find
the height of the cone if the slant height is 4 and the
radius is 2. Round to the nearest tenth.
36. CHALLENGE Solve
.
ANSWER: 3
38. SHORT RESPONSE Zach needs to drill a hole at
A, B, C, D, and E on circle P.
ANSWER: If Zack drills holes so that m APE = 110º and the
other four angles are congruent, what is m CPD?
or ≈ 3.5
30. PACKAGING A cylindrical container of chocolate
drink mix has a volume of 162 cubic inches. The
radius r of the container can be found by using the
formula
, where V is the volume of the
ANSWER: 62.5°
40. What is the slope of a line that is parallel to the line?
container and h is the height.
a. If the radius is 2.5 inches, find the height of the
container. Round your answer to the nearest
hundredth.
b. If the height of the container is 10 inches, find the
radius. Round to the nearest hundredth.
F −3
ANSWER: a. 8.25 in.
b. 2.27 in.
G H 32. REASONING Which equation has the same
solution set as
? Explain.
J 3
ANSWER: H
A. 42. ELECTRICITY The voltage V required for a
B. 4 = x + 2
circuit is given by
, where P is the power
in watts and R is the resistance in ohms. How many
more volts are needed to light a 100-watt light bulb
than a 75-watt light bulb if the resistance of both is
110 ohms?
C. ANSWER: The solution of the given equation is 2. Choice B is
the only equation that is true when x = 2.
ANSWER: about 14
34. OPEN ENDED Write a radical equation with a
variable on each side. Then solve the equation.
Simplify each expression.
ANSWER: Sample answer:
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36. CHALLENGE Solve
ANSWER: 44. .
ANSWER: Page 2
than a 75-watt light bulb if the resistance of both is
110 ohms?
56. 12
ANSWER: Yes; 12 is a real number and therefore a monomial.
10-4ANSWER: Radical Equations
about 14
Simplify each expression.
58. a − 2b
ANSWER: No; a – 2b shows subtraction, not multiplication
alone of numbers and variables.
44. ANSWER: 60. 46. ANSWER: No;
ANSWER: has a variable in the denominator.
Simplify.
2
62. 9
48. ANSWER: 81
ANSWER: 5
64. 4
Factor each trinomial, if possible. If the
trinomial cannot be factored using integers,
write prime .
2
50. 2x + 7x + 5
ANSWER: 1024
66. ANSWER: ANSWER: (2x + 5) (x + 1)
2
52. 5d + 6d − 8
ANSWER: (5d − 4) (d + 2)
2
54. 9g − 12g + 4
ANSWER: (3g – 2)(3g – 2)
Determine whether each expression is a
monomial. Write yes or no. Explain.
56. 12
ANSWER: Yes; 12 is a real number and therefore a monomial.
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58. a − 2b
ANSWER: Page 3