10-4 Radical Equations
21. RIDES The amount of time t, in seconds, that it takes a simple pendulum to complete a full swing is called the
period . It is given by
, where
is the length of the pendulum, in feet.
a. The Giant Swing completes a period in about 8 seconds. About how long is the pendulum’s arm? Round to the
nearest foot.
b. Does increasing the length of the pendulum increase or decrease the period? Explain.
ANSWER: a. 52 ft
b. Increases; sample answer: If the length is longer, the quotient and square root will be a greater number than
before.
Solve each equation. Check your solution.
22. ANSWER: no solution
23. ANSWER: no solution
24. ANSWER: 25. ANSWER: 235.2
26. ANSWER: 11
27. ANSWER: 3
, where h is the height of the
28. CCSS REASONING The formula for the slant height c of a cone is
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
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the nearest
27. 10-4ANSWER: Radical Equations
3
, where h is the height of the
28. CCSS REASONING The formula for the slant height c of a cone is
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.
ANSWER: or ≈ 3.5
.
29. MULTIPLE REPRESENTATIONS Consider
a. GRAPHICAL Clear the Y= list. Enter the left side of the equation as Y1 =
. Enter the right side of
the equation as Y2 = x − 7. Press GRAPH.
b. GRAPHICAL Sketch what is shown on the screen.
c. ANALYTICAL Use the intersect feature on the CALC menu to find the point of intersection.
d. ANALYTICAL Solve the radical equation algebraically. How does your solution compare to the solution from
the graph?
ANSWER: a.
b. See students’ work.
c.
d. about 10.83; They are the same.
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 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.
ANSWER: a. 8.25 in.
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b. 2.27
in.
31. CCSS CRITIQUE Jada and Fina solved
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. Is either of them correct? Explain.
10-4 Radical Equations
d. about 10.83; They are the same.
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 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.
ANSWER: a. 8.25 in.
b. 2.27 in.
31. CCSS CRITIQUE Jada and Fina solved
. Is either of them correct? Explain.
ANSWER: Jada; Fina had the wrong sign for 2b in the fourth step.
32. REASONING Which equation has the same solution set as
? Explain.
A. B. 4 = x + 2
C. ANSWER: The solution of the given equation is 2. Choice B is the only equation that is true when x = 2.
33. REASONING Explain how solving
is different from solving .
ANSWER: Sample answer: In the first equation, you have to isolate the radical first by subtracting 1 from each side. Then
square each side to find the value of x. In the second equation, the radical is already isolated, so square each side to
start. Then subtract 1 from each side to solve for x.
36. CHALLENGE Solve
.
ANSWER: 3
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