Cogito
Grade 8 Math · Chapter 8 · Lesson 1
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
What this lesson teaches
The child evaluates square and cube roots and distinguishes rational from irrational numbers.
- A square root undoes squaring; a cube root undoes cubing.
- A rational number can be written as a fraction of integers.
- An irrational number cannot, and its decimal never ends or repeats.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Calculating in Scientific Notation: (4 × 10⁵) × (2 × 10³). What is the exponent?
Answer 8
Why 8.
Review — Zero and Negative Exponents: What is 10⁻²? Give it as a decimal.
Answer 0.01
Why 0.01.
Warm Up
Straightforward practice. Get the method working first.
4 problemsWhat is √100?
Answer 10
Why 10.
What makes a number irrational?
Answer It cannot be written as a fraction of integers.
Why No fraction of integers equals it.
What is √144?
Answer 12
Why 12 × 12.
What is the cube root of 125?
Answer 5
Why 5 × 5 × 5.
Build It Up
The same ideas with more to keep track of.
2 problems√20 is between which whole number and the next?
Answer 4
Why 16 and 25.
Is √2 rational?
Answer No. It is irrational.
Why It cannot be written as a fraction.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Root: What is √81?
Answer 9
Why 9.
The Cube Root: What is the cube root of 64?
Answer 4
Why 4.