Radical Expressions and Surds
Roots of integers and rationals; simplify surds (√50=5√2); multiply and add/subtract surds; rationalise denominators using conjugates; convert between radical and rational exponent form.
11 worksheetsRead the explainer →
- 1Roots of IntegersEvaluate square, cube and higher roots of positive integers; identify perfect powers.adaptive
- 2Roots of Rational NumbersEvaluate square and cube roots of fractions; simplify radical expressions involving fractions.adaptive
- 3Find Roots Using a CalculatorUse calculator to find decimal approximations of surds; compare surd size.adaptive
- 4Simplify Radical ExpressionsExtract perfect square factors: sqrt(50)=5sqrt(2), sqrt(72)=6sqrt(2). Simplify fully.adaptive
- 5Simplify Radical Expressions with FractionsSimplify sqrt(a/b) = sqrt(a)/sqrt(b); rationalise simple denominators; sqrt(1/3)=sqrt(3)/3.adaptive
- 6Multiply Radical ExpressionsMultiply surds: sqrt(2)*sqrt(8)=4; 2sqrt(3)*3sqrt(5)=6sqrt(15); simplify results.adaptive
- 7Add and Subtract Radical ExpressionsAdd/subtract like surds: 2sqrt(3)+5sqrt(3)=7sqrt(3); simplify before combining.adaptive
- 8Simplify Using Distributive PropertyExpand sqrt(2)(sqrt(8)+3); 2sqrt(3)(sqrt(3)-4); distribute over surd expressions.adaptive
- 9Simplify Using ConjugatesRationalise denominators using conjugate: 1/(sqrt(3)+sqrt(2))=(sqrt(3)-sqrt(2))/1.adaptive
- 10Simplify Radical Expressions Mixed ReviewMixed review of all surd skills: simplify, multiply, add/subtract, rationalise.adaptive
- 11Convert Between Rational Exponents and RadicalsWrite sqrt(x) as x^(1/2); write x^(2/3) as cube_root(x^2); convert in both directions.adaptive