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Cogito

Integrated Math 3 · Chapter 3 · Lesson 2

Practice Worksheet

Solving Radical Equations

Squaring can invent solutions.

12 problems · about 21 minutes · A-REI.A.2

NameDate

Figure — use these to answer the problems

The square root curve never dips below the axis. A solution requiring a negative root cannot exist.
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y = 1√x + 0
  • Point(4, 2)
a, coefficient1
Point on the curve4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. √(x − 2) = 5. What is x?

    Answer

  2. Why can squaring introduce extraneous solutions?

    • Squaring destroys the sign, so −3 and 3 become the same.
    • They come from arithmetic mistakes.

  3. √x = 7. What is x?

    Answer

  4. √(x − 3) = 4. What is x?

    Answer

  5. √x = −2. How many solutions?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. The cube root of x = 2. What is x?

    Answer

  2. Do cube root equations produce extraneous solutions? 1 yes, 0 no.

    Answer

  3. √(2x) = 6. What is x?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the solving process in order.

    Write 1 to 4 in the boxes to put these in order.

    • Isolate the radical on one side.
    • Raise both sides to the matching power.
    • Solve the resulting equation.
    • Check every candidate in the original and reject failures.

  2. √(x + 1) = 3. What is x?

    Answer

  3. The Solve

    √x = 5. What is x?

    Answer

  4. The Rejection

    √(x + 6) = x. How many valid solutions?

    Answer