Number & Sets · SS 2
Rules of surds
Simplify square roots and clear roots from the bottom of a fraction (rationalising).
- √(ab) = √a × √b
- √(ab) = √a√b
- 1√a = √aa
What the letters mean
- a, b
- positive numbers
Worked example
Simplify √72.
Step 1: Find the largest square factor of 72
72 = 36 × 2
Step 2: Split the root
√72 = √36 × √2 = 6√2
Step 3: Check with a calculator
6√2 ≈ 6 × 1.414 = 8.49 and √72 ≈ 8.49 ✓
Final answer: 6√2 (about 8.49)
√a + √b is NOT √(a + b): √9 + √16 = 7, but √25 = 5.
See it
Play with this picture from the Simplifying Surds lesson.
√72 — 72 little squares
Square numbers that divide 72:
Pick a square number to regroup the 72 squares.
Number under the root
72