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Cogito

Algebra 2 · Chapter 5 · Lesson 1

Practice Worksheet

Rational Exponents and Radical Equations

A fractional exponent is a root.

10 problems · about 20 minutes · N-RN.A.1, N-RN.A.2, A-REI.A.2

NameDate

Figure — use these to answer the problems

The square root curve exists only where the inside is not negative.
-8-8-6-6-4-4-2-222446688
y = 1√x + 0
  • Point(4, 2)
Stretch1
Shift up by0
Read at x4
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Direct, Inverse, and Joint Variation”

    y varies inversely with x, and y = 10 when x = 3. What is k?

    Answer

  2. From “Adding and Simplifying Rational Expressions”

    (x² − 36)/(x − 6) simplifies to x + what?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. What is 81^(1/2)?

    Answer

  2. In x^(m/n), which number gives the root?

    • The bottom one, n.
    • The top one, m.

  3. What is 25^(1/2)?

    Answer

  4. What is 8^(2/3)?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. What is 64^(1/3)?

    Answer

  2. Must you check answers after squaring both sides?

    • Yes.
    • No.

Stretch Yourself

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

2 problems

  1. The Exponent

    What is 16^(1/2)?

    Answer

  2. The Cube Root

    What is 27^(1/3)?

    Answer