AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S1_2024Radical Equations and Extraneous Roots

Radical Equations and Extraneous Roots — Unit test Answers

15 verified answers
1
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What is the following simplified product? Assume

Question illustration
A
3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared + 8 x Superscript 5 Baseline StartRoot 10 x EndRoot
Option A
B
3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot + 8 x Superscript 5 Baseline StartRoot 10 EndRoot
Option B
C
3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 EndRoot
Option C
D
3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 x EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 x EndRoot
Option D
2
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What is the following product? Assume

Question illustration
A
6 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
Option A
B
6 StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
Option B
C
6 y squared StartRoot 10 EndRoot + 4 StartRoot 5 y EndRoot
Option C
D
3 y squared StartRoot 10 EndRoot + 12 StartRoot 5 y EndRoot
Option D
3

What is the following product? Assume

Question illustration
A
x StartRoot x EndRoot
Option A
B
RootIndex 12 StartRoot x Superscript 5 EndRoot
Option B
C
x (RootIndex 12 StartRoot x Superscript 5 EndRoot)
Option C
D
x6
4

Which expression is equivalent to ? Assume and .

Question illustration
A
StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 2 c cubed EndFraction
Option A
B
StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a squared c cubed EndFraction
Option B
C
StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 6 c cubed EndFraction
Option C
D
StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a c EndFraction
Option D
5

Which expression is equivalent to ?

Question illustration
A
StartFraction x Superscript one-half baseline Over y z squared EndFraction
Option A
B
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
Option B
C
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
Option C
D
StartFraction x z squared Over y Superscript one-half EndFraction
Option D
6

The formula relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth. What is the length of a pendulum that makes one full swing in 2.2 seconds? Use 3.14 for .

Question illustration
A
2 feet
B
4 feet
C
11 feet
D
19 feet
7

What is the following sum?

Question illustration
A
6 b squared (RootIndex 3 StartRoot 2 a EndRoot)
Option A
B
12 b squared (RootIndex 3 StartRoot 2 a EndRoot
Option B
C
6 b squared (RootIndex 6 StartRoot 2 a EndRoot)
Option C
D
12 b squared (RootIndex 6 StartRoot 2 a EndRoot)
Option D
8

What is the simplified form of the following expression?

Question illustration
A
StartRoot 3 EndRoot
Option A
B
9 StartRoot 3 EndRoot
Option B
C
11 StartRoot 3 EndRoot
Option C
D
15 StartRoot 3 EndRoot
Option D
9

What is the following product?

Question illustration
A
6 StartRoot 2 EndRoot minus 2 StartRoot 30 EndRoot + 6 minus 2 StartRoot 15 EndRoot
Option A
B
6 StartRoot 3 EndRoot minus 6 StartRoot 5 EndRoot
Option B
C
3 StartRoot 2 EndRoot minus StartRoot 22 EndRoot + 2 StartRoot 3 EndRoot minus 4
Option C
D
2 StartRoot 3 EndRoot + 6 minus 2 StartRoot 15 EndRoot
Option D
10

What values of c and d make the equation true? Assume and

Question illustration
A
c = 1, d = 3
B
c = 1, d = 9
C
c = 2, d = 8
D
c = 2, d = 9
11

Jamal simplified the expression where and . Which describes the error Jamal made?

Question illustration
A
He should have written the square root of in the answer as , not .
Option A
B
He should have written the square root of in the answer as , not .
Option B
C
He should have written the 5 inside of the radical in the answer.
D
He should have written the 3 outside of the radical in the answer.
12

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after years?

Question illustration
A
$2,500
B
$9,159
C
$22,827
D
$23,791
13

What is the solution of ?

Question illustration
A
x = –10
B
x = 3
C
x = –10 or x = 3
D
no solution
14

Which expression is equivalent to ? Assume x 0.

Question illustration
A
StartFraction x cubed StartRoot 2 EndRoot Over 2 EndFraction
Option A
B
StartFraction 4 StartRoot 2 EndRoot Over x cubed EndFraction
Option B
C
StartFraction StartRoot 2 EndRoot Over 2 x cubed EndFraction
Option C
D
StartFraction 2 StartRoot 2 EndRoot Over x cubed EndFraction
Option D
15

Which function has a domain of and a range of ?

Question illustration
A
y = StartRoot x minus 5 EndRoot + 3
Option A
B
y = StartRoot x + 5 EndRoot minus 3
Option B
C
y = negative StartRoot x minus 5 EndRoot + 3
Option C
D
y = negative StartRoot x + 5 EndRoot minus 3
Option D

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