Irrational Numbers
11-5Square Roots of Variable Expressions
Overview
√(x²) = |x|. For a ≥ 0 and b ≥ 0: √(ab) = √a · √b.
Key ideas
- Factor out perfect squares.
- Assume variables are non-negative unless told otherwise.
- Combine like radicals only when radicands match.
Worked examples
Example 1
Problem. Simplify √(x^4).
Solution. x² (x ≥ 0)
Example 2
Problem. Simplify √(50).
Solution. √(25·2) = 5√2
Practice
Try each one. Click Show answer when ready.
- 1.
Simplify √(y^6).
- 2.
Simplify √(75).
- 3.
Simplify √(9x^2).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify √(25x⁶y²).
- 2.
Simplify √(18a⁴b³).