Radical Expressions
11-7Multiplying, Dividing, and Simplifying Radicals
Overview
√a · √b = √(ab); √a / √b = √(a/b). Simplify by extracting perfect squares.
Key ideas
- Combine under one radical, then simplify.
- Rationalize a denominator by multiplying by √(same) / √(same).
- Reduce final radicand.
Worked examples
Example 1
Problem. √3 · √12
Solution. √36 = 6
Example 2
Problem. Rationalize 1/√2.
Solution. √2/2
Practice
Try each one. Click Show answer when ready.
- 1.
√5 · √20
- 2.
Simplify √(45).
- 3.
Rationalize 3/√3.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify √12 · √27.
- 2.
Simplify (√50)/(√2).