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Cogito

Grade 8 Math · Chapter 8 · Lesson 3

Practice Worksheet

Placing an Irrational Number

Trapping √2 between two numbers you know.

10 problems · about 19 minutes · 8.NS.A.2

NameDate

Figure — use these to answer the problems

Place a value between the whole numbers that trap it.
012345

1

The value1
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

3 problems

  1. From “Cube Roots”

    Cube root of 216?

    Answer

  2. From “Square Roots and Irrational Numbers”

    What is √100?

    Answer

  3. From “Calculating in Scientific Notation”

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

    Answer

Warm Up

Straightforward practice. Get the method working first.

3 problems

  1. √40 lies between which two whole numbers? Give the smaller.

    Answer

  2. √8 lies between which two whole numbers? Give the smaller.

    Answer

  3. √30 lies between which two whole numbers? Give the smaller.

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. √49 exactly. What is it?

    Answer

  2. Does the decimal for √2 ever repeat? 1 for yes, 0 for no.

    Answer

Stretch Yourself

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

2 problems

  1. The Trap

    √5 lies between which two whole numbers? Give the smaller one.

    Answer

  2. The Bigger One

    √20 lies between which two whole numbers? Give the smaller one.

    Answer