Radical Equations and Extraneous Roots

Question 1

Solve:

Revolt · Accepted Answer

x = –4 or x = 4

Question 2

Solve:

Revolt · Accepted Answer

s = 7

Question 3

Solve:

Revolt · Accepted Answer

x = 10

Question 4

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

0.155 km

Question 5

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 6

in.

Revolt · Accepted Answer

9

Question 7

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 8

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

Revolt · Accepted Answer

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

Question 9

Solve:

Revolt · Accepted Answer

Answer image: https://r09.core.learn.edgenuity.com//media.edgenuity.com/EVresources/3111-09-09-20-02-task/mc002-3.jpg

Question 10

Did your explanation include the following?

Revolt · Accepted Answer

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

Radical Equations and Extraneous Roots Answers

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