Only like surds add
, but . Simplify each surd first to spot like terms.
Pull out the largest square factor
, so . Take out the biggest perfect square in one go.
Rationalise the denominator
For multiply top and bottom by ; for multiply by the conjugate .
Drawn from real examiner reports.
Typing the surd into a calculator
When working is requested, entering the fraction and copying the decimal display scores no marks.
A commonly reported examiner note records this approach "scored no marks as working was requested".
Rationalising with the wrong multiplier
Using an incorrect multiplier for a binomial denominator — e.g. instead of the correct conjugate, or the wrong sign.
Errors with the rationalising multiplier (typically $\sqrt{2}-1$) were seen on a recent higher-tier paper.
Writing only the integer, no surd
Giving just a whole number with no surd factor (and no working) is not credited.
A commonly reported examiner note records that writing only "5" earned nothing without the surd shown.
Not simplifying fully before adding
. Simplify each surd first so like terms appear: . Adding under one root, or leaving unlike surds, loses the mark.
Dropping the middle term when squaring
Expanding needs the cross term: . Writing just and dropping is a frequent error.
Keep in surd form, show each step
Never round to a decimal mid-question, and show the surd manipulation — examiners require the working for full marks.
Multiply by the conjugate, then simplify
For a binomial denominator , multiply top and bottom by the conjugate (same terms, opposite sign) — this is a difference of two squares that clears the surd. Then cancel any common factor to reach .
Simplify the final surd answer fully
After rationalising you may get something like . Cancel the common factor: . An un-simplified surd can cost the final accuracy mark.
Split off the largest perfect-square factor: Doing it in one step (not , which isn't fully simplified) is cleaner and avoids errors.
What is (√q)²?
Simplify , giving your answer in the form .
