Surds · Year 11
In Year 11 you learn: multiplying and dividing surds.
A surd is a square root that does not come out as a whole number, like √2 or √12. Leaving answers as surds keeps them exact instead of rounding. We simplify surds by taking out square factors, and rationalise denominators so that no root is left on the bottom of a fraction.
Key facts
- √(ab) = √a × √b and √(a/b) = (√a)/(√b).
- √a × √a = a.
- Simplify using the biggest square factor: √72 = √36 × √2 = 6√2.
- Only like surds can be added: 3√5 + 2√5 = 5√5, but √2 + √3 stays as it is. √a + √b ≠ √(a + b).