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Cogito

Grade 8 Math · Chapter 8 · Lesson 1

Practice Worksheet

Square Roots and Irrational Numbers

Numbers that never settle down.

10 problems · about 19 minutes · 8.NS.A.1, 8.NS.A.2, 8.EE.A.2

NameDate

Figure — use these to answer the problems

A perfect square makes a perfect square. Try a number that does not.

5 × 5 = 25

Rows5
In each row5
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Calculating in Scientific Notation”

    (4 × 10⁵) × (2 × 10³). What is the exponent?

    Answer

  2. From “Zero and Negative Exponents”

    What is 10⁻²? Give it as a decimal.

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. What is √100?

    Answer

  2. What makes a number irrational?

    • It cannot be written as a fraction of integers.
    • It is very large.

  3. What is √144?

    Answer

  4. What is the cube root of 125?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. √20 is between which whole number and the next?

    Answer

  2. Is √2 rational?

    • No. It is irrational.
    • Yes.

Stretch Yourself

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

2 problems

  1. The Root

    What is √81?

    Answer

  2. The Cube Root

    What is the cube root of 64?

    Answer