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

in.

Revolt · Accepted Answer

8

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

Checking the solutions in the original equation verifies [image 1] ; however, [image 2] is extraneous.

Question 8

Solve:

Revolt · Accepted Answer

mc002-3.jpg

Radical Equations and Extraneous Roots Answers

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