Radical Equations and Extraneous Roots

Question 1

Solve:

Revolt · Accepted Answer

C: x = –4 or x = 4

Question 2

Solve:

Revolt · Accepted Answer

B: x = 10

Question 3

The speed that a tsunami (tidal wave) can travel is modeled by the equationwhere S is the speed in kilometers per hour, and d is the average depth of the water in kilometers.A tsunami is traveling at 140 km/hr. What is the approximate average depth of the water?

Revolt · Accepted Answer

C: 0.155 km

Question 4

The formula gives the time it takes in seconds, T, for a pendulum to make one full swing back and forth, where L is the length of the pendulum, in feet.To the nearest foot, what is the length of a pendulum that makes one full swing in 1.9 s? Use 3.14 for . ft

Revolt · Accepted Answer

3

Question 5

in.

Revolt · Accepted Answer

9

Question 6

Do you agree? Explain why or why not.

Revolt · Accepted Answer

I do not agree with the student. While solving the equation results in x  4, this is an extraneous solution. When you substitute 4 back into the original equation, you get sqrt(2(4)  1)  3  0, which simplifies to 3  3  0, or 6  0. Since this is a false statement, x  4 is not a solution. Furthermore, the equation sqrt(2x  1)  3 has no real solution because a principal square root cannot be negative.

Question 7

Do you agree with the student? Explain why or why not.

Revolt · Accepted Answer

B: Checking the solutions in the original equation verifies ; however, is extraneous.

Question 8

Solve:

Revolt · Accepted Answer

B: s = 7

Question 9

Solve:

Revolt · Accepted Answer

C:

Question 10

Did your explanation include the following?

Revolt · Accepted Answer

A: I do not agree with the student because there is no real solution.; B: Solving the equation only gives possible solutions, but you must check them in the original equation.; C: Checking the solution in the original equation shows that 4 is an extraneous solution.

Radical Equations and Extraneous Roots Answers

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