Rational, irrational and surds
Pages
Rational and irrational numbers
Which numbers are one integer over another, and where π and surds sit.
Simplifying surds
Extracting the largest square factor to write a√b, and comparing surds.
Adding and subtracting surds
Collecting like surds after simplifying every term.
Multiplying surds
Multiplying roots and coefficients separately, then simplifying the result.
Squaring a surd
Why a root times itself gives the number back, and what a coefficient does.
Dividing surds
Dividing under a single root, and simplifying quotients with coefficients.
Expanding brackets with surds
Single and double brackets, squaring one, and the difference of two squares.
Rationalising a denominator
Clearing a single surd from the bottom of a fraction by multiplying by one.
Rationalising with a conjugate
Clearing a two-term surd denominator by reversing the middle sign and expanding.
Practice
Simplifying surds
Extracting the largest square factor to write a√b, and comparing surds.
PracticeAdding and subtracting surds
Collecting like surds after simplifying every term.
PracticeMultiplying surds
Multiplying roots and coefficients separately, then simplifying the result.
PracticeSquaring a surd
Why a root times itself gives the number back, and what a coefficient does.
PracticeDividing surds
Dividing under a single root, and simplifying quotients with coefficients.
PracticeExpanding brackets with surds
Single and double brackets, squaring one, and the difference of two squares.
PracticeRationalising a denominator
Clearing a single surd from the bottom of a fraction by multiplying by one.
PracticeSurds review
Simplifying and rationalising denominators.