A surd is an irrational root that cannot be written as an exact decimal. In this topic you will learn how to simplify surds, use the basic rules for multiplying and dividing, add and subtract like surds, and rationalise the denominator.
What is a surd?A surd is a root of a number that is irrational. Examples: √2, √3, √5.√4 = 2 …
View LessonRulesMultiplying: √a × √b = √(ab)Dividing: √a ÷ √b = √(a/b)Examples√2 × √8 = √16 = 43√5 × 2√2 = …
View LessonLike surdsYou can only add or subtract 'like' surds, just like like terms in algebra.2√3 + 5√3 = 7√36√2 - …
View LessonWhy rationalise?It is standard to remove surds from the bottom of a fraction.Type 1: Single surdMultiply top and bottom by …
View LessonSimplify:√3 × √122√5 × 3√2√6 × √15√50 ÷ √28√20 ÷ 4√5(√6)2
View Exercise Submit ExerciseSimplify:3√5 + 2√57√3 - 4√3√12 + √27√45 - √202√8 + √18 - √25√6 - 2√24 + √54
View Exercise Submit ExerciseRationalise and simplify:1/√53/√2√6/√31/(3+√2)4/(5-√3)(√5+1)/(√5-1)
View Exercise Submit Exercise