Students learn how to rationalise a denominator using the complex conjugate.
Prerequisite Knowledge
Know and apply the following rules of indices:
Multiplication Rule na × nb = na + b
Division Rule na × nb = na + b
Power Rule (na)b
Power of Zero
Evaluate expressions with fractional and negative powers
Simplify a surd
Rationalise a denominator in the form 1/√a
Success Criteria
Understand and be able to use the laws of indices for all rational exponents.
Use and manipulate surds, including rationalising the denominator.
Teaching Points
Simplifying surds at the start of a problem often makes future working much simpler.
Students need to:
evaluate expressions involving numerical and algebraic bases with a fractional and negative power.
apply the rules of indices to fractional and negative powers.
know how the complex conjugate is used to rationalise a denominator.
Misconceptions
Students often leave surds un-simplified especially when rationalising a denominator using the complex conjugate.
1/2x is often written incorrectly written as 2x-1 rather than (2x)-1.
√a + √b is often incorrectly simplified to √(a +b)
Students often struggle to evaluate indices involving both a fractional and negative power. This is especially true when the base involves an algebraic and numerical term.