Review for MA098
Radicals
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) A cosmetic surgeon is planning a skin graft operation for a patient. She plans to remove a
rectangular area of skin measuring 175 square millimeters from under the patient's arm.
Write this area in simplified radical form.
Simplify. Assume that all variables represent positive numbers.
2) 8k7 q8
Solve.
1)
2)
3) If y varies directly as the cube of x, and y = 16 when x = 20, find y when x = 15.
3)
Find the exact length of the missing side of a right triangle with sides a, b, and c, where c is the hypotenuse.
4) a = 35, b = 10
4)
Find the root.
6
5) 64
5)
Use the Pythagorean theorem to find the length of the third side of the right triangle. Leave any irrational answers in
radical form.
6)
6)
6
c
8
Simplify. Be sure to rationalize all denominators. Assume that all variables represent positive real numbers.
1
7)
7)
11x
Solve the problem.
8) A fence is to be installed around a triangular garden with sides measuring (4 +
(4 + 2) feet by (6 - 3) feet. Find the exact distance to be fenced.
3) feet by
8)
Use a calculator or the square root table to approximate the square root to the nearest thousandth.
9) 7
9)
Combine the following, if possible.
10) -8 7 + 4 7
10)
11) 19 x8 + x x6
11)
1
Solve.
12) -4 7 - 5 175
12)
13) If the force acting on an object stays the same, then the acceleration of the object is inversely
proportional to its mass. If an object with a mass of 20 kilograms accelerates at a rate of
2 meters per second per second by a force, find the rate of acceleration of an object with a
mass of 5 kilograms that is pulled by the same force.
13)
Multiply and simplify any radicals in your answer. Assume that all variables represent positive real numbers.
14) 6(5 12 - 7 3 )
14)
Simplify. Assume that all variables represent positive numbers.
15) 16x18y32z 2
15)
Simplify. Be sure to rationalize all denominators. Assume that all variables represent positive real numbers.
168
16)
16)
6
Use a calculator or the square root table to approximate the square root to the nearest thousandth.
17) - 98
Solve.
18) If y varies directly as x, and y = 2 when x = 7, find y when x = 49.
Find the square root.
19) 4.84
17)
18)
19)
Simplify. Be sure to rationalize all denominators. Assume that all variables represent positive real numbers.
2x
20)
20)
6
Solve.
21) If the resistance in an electrical circuit is held constant, the amount of current flowing
through the circuit is directly proportional to the amount of voltage applied to the circuit.
When 9 volts are applied to a circuit, 225 milliamperes of current flow through the circuit.
Find the new current if the voltage is changed to 5 volts.
Simplify. Assume that all variables represent positive numbers.
22) y9
23)
81x2 + 18x + 1
21)
22)
23)
Combine the following, if possible.
24) 25 5 - 12 5
24)
2
Simplify. Be sure to rationalize the denominator. Assume that all variables represent positive real numbers.
x-6
25)
25)
x+6
Multiply and simplify any radicals in your answer. Assume that all variables represent positive real numbers.
26) (5x 6x)(6 2x)
26)
Simplify. Be sure to rationalize all denominators. Assume that all variables represent positive real numbers.
75
27)
27)
3
Find the square root.
28) 324
28)
Simplify. Be sure to rationalize all denominators. Assume that all variables represent positive real numbers.
10
29)
29)
250
Find the exact length of the missing side of a right triangle with sides a, b, and c, where c is the hypotenuse.
30) b = 5, c = 12
30)
Multiply and simplify any radicals in your answer. Assume that all variables represent positive real numbers.
31) (3 y)(3 y)
31)
Find the root.
3
32) -125
32)
Solve for the variable.
33) p2 - 3p + 4 = p - 1
33)
Simplify. Assume that all variables represent positive numbers.
34) 576x2 + 192x + 16
34)
Multiply.
35) (3 2 + 3)2
35)
Solve the problem.
36) A tree is 12 feet tall. A wire that stretches from a point that is 9 feet from the base of the tree
to the top of the tree is 225 feet long. Exactly how many feet long is the wire?
Solve.
37) The amount of time it takes a swimmer to swim a race is inversely proportional to the
average speed of the swimmer. A swimmer finishes a race in 300 seconds with an average
speed of 4 feet per second. Find the average speed of the swimmer if it takes 400 seconds to
finish the race.
3
36)
37)
Multiply.
38) (5 a)( ab)(2 b)
Solve.
38)
39) The amount of water used to take a shower varies directly as the amount of time that the
shower is in use. A shower lasting 16 minutes requires 8 gallons of water. Find the
amount of water used in a shower lasting 5 minutes.
39)
Simplify. Be sure to rationalize the denominator. Assume that all variables represent positive real numbers.
x - 25
40)
40)
x+5
Combine and simplify.
41) 72a + 363a +
50a + 10 147a
41)
Find the square root.
121
42)
81
42)
Simplify. Be sure to rationalize the denominator. Assume that all variables represent positive real numbers.
5
43)
43)
2+ 7
Solve.
44) The amount of water used to take a shower is directly proportional to the amount of time
that the shower is in use. A shower lasting 24 minutes requires 12 gallons of water. Find
the amount of water used in a shower lasting 4 minutes.
44)
Simplify. Be sure to rationalize all denominators. Assume that all variables represent positive real numbers.
3
45)
45)
x
Simplify.
46)
64x10yz 5
46)
Find the root.
3
47) 27
47)
Simplify. Assume that all variables represent positive numbers.
48) 36x8 y2
48)
Solve.
49) Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle
with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the
pole to a stake 8 feet from the bottom of the pole. To the nearest tenth of a foot, find the
length of the rope.
4
49)
50) For a resistor in a direct current circuit that does not vary its resistance, the power that a
resistor must dissipate is directly proportional to the square of the voltage across the
1
resistor. The resistor must dissipate
watt of power when the voltage across the resistor
16
is 13 volts. Find the power that the resistor must dissipate when the voltage across it is 39
volts.
5
50)
Answer Key
Testname: RADICALS
1) 5 7 square millimeters
2) 2k3 q4 2k
3)
27
4
4) 5 53
5) 2
6) 10
11x
7)
11x
8) (14 + 2) feet
9) 2.646
10) -4 7
11) 20x4
12) -29 7
13) 8 meters per second per second
14) 9 2
15) 4x9 y16z
16) 2 7
17) -9.899
18) 14
19) 2.2
3x
20)
3
21) 125 milliamperes
22) y4 y
23) 9x + 1
24) 13 5
x - 12 x + 36
25)
x - 36
26) 60x2 3
27) 5
28) 18
10
29)
5
30) 7
31) 9y
32) -5
33) p = 3
34) 4(6x + 1)
35) 27 + 18 2
36) 15 ft
37) 3 feet per second
38) 10ab
39) 2.5 gallons
40) x - 5
41) 11 2a + 81 3a
6
Answer Key
Testname: RADICALS
42)
11
9
43) 7 - 2
44) 2 gallons
3 x
45)
x
46) 8x5 z 2 yz
47) 3
48) 6x4 y
49) 10 ft.
9
watt
50)
16
7