A surd is a square root that can't simplify to a whole number — like √2 or √7. They're irrational.
Quick check
Simplify √50
Working with surds
- Simplify: pull out perfect-square factors — √72 = √(36·2) = 6√2.
- Multiply: √a · √b = √(ab).
- Rationalise: clear a surd from the denominator by multiplying top and bottom by it — 1/√3 = √3/3.
- Surds are irrational — their decimals never terminate or repeat.
Your turn
Rationalise the denominator of 6/√2.
Watch out
√(a + b) ≠ √a + √b. √(9 + 16) = √25 = 5, not 3 + 4 = 7. You can split a root over multiplication, never over addition.
Simplify
Pull perfect squares out: √50 = √(25·2) = 5√2.
Rationalise the denominator
Multiply top and bottom by the surd: 1/√2 = √2/2.