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Cogito

Integrated Math 3 · Chapter 3 · Lesson 1

Practice Worksheet

Rational Exponents and Radicals

A fraction in the exponent is a root.

12 problems · about 21 minutes · N-RN.A.1, N-RN.A.2

NameDate

Figure — use these to answer the problems

The square root curve is x to the one half. It rises quickly then flattens.
-8-8-6-6-4-4-2-222446688
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. What is 27^(2/3)?

    Answer

  2. In x^(m/n), what does the denominator give?

    • The root to take.
    • The power to raise to.

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

    Answer

  4. What is 27^(1/3)?

    Answer

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

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. What is 9^(3/2)?

    Answer

  2. What is 4^(−1/2), as a decimal?

    Answer

  3. Does an odd root accept negative inputs? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Match each expression with its value.

    Draw a line from each item on the left to its match on the right.

    • 8 to the one third
    • 8 to the two thirds
    • 8 to the zero
    • Two
    • Four
    • One

  2. What is 32^(1/5)?

    Answer

  3. The Power

    What is 8^(2/3)?

    Answer

  4. The Root

    What is 16^(1/2)?

    Answer