Irrational Numbers
11-4Irrational Square Roots
Overview
If n is a positive integer that is not a perfect square, √n is irrational.
Key ideas
- Irrationals have non-terminating, non-repeating decimals.
- √2, √3, √5, π are classic examples.
- Approximate with a calculator when needed.
Worked examples
Example 1
Problem. Approximate √7 to 2 decimals.
Solution. ≈ 2.65
Example 2
Problem. Is √16 irrational?
Solution. No, equals 4.
Practice
Try each one. Click Show answer when ready.
- 1.
√50 between which consecutive integers?
- 2.
Is √100 rational?
- 3.
Approximate √20.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Between which two consecutive integers does √50 lie?
- 2.
Estimate √27 to the nearest tenth.