Rational Numbers
11-3Rational Square Roots
Overview
√(a²) = |a|. A square root is rational when the radicand is a perfect square of a rational number.
Key ideas
- √25 = 5; √(1/4) = 1/2.
- Square roots of perfect squares are rational.
- Otherwise the root is irrational.
Worked examples
Example 1
Problem. Evaluate √81.
Solution. 9
Example 2
Problem. Evaluate √(9/16).
Solution. 3/4
Practice
Try each one. Click Show answer when ready.
- 1.
√144
- 2.
√(25/49)
- 3.
√0.04
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify √72.
- 2.
Simplify √200.