Young Geniuses · Ages 13 to 14
Four Operations with Surds MCQ
Add, subtract, multiply and divide surds. Five levels of printable practice with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Four Operations with Surds MCQ
Surds behave like algebra, not like decimals, and the single most common error is treating them like neither — writing that root two plus root three is root five. It is not, and no amount of arithmetic makes it so: unlike surds combine no more than x and y do. This worksheet is built so that error is impossible to model. Addition and subtraction questions use like surds only, where the coefficients add and the radical stays put; multiplication combines the radicands and then simplifies; and division is constructed so the result is exact. Every answer is held as a coefficient and a square-free radicand, and the options are compared in that canonical form rather than as text or as decimal approximations — which is what lets the worksheet guarantee that exactly one option is mathematically equal to the question and the other three genuinely are not. The distractors are the real errors: adding the radicands as well as the coefficients, and multiplying without simplifying. The levels move from like-surd addition, through subtraction, to multiplication, to division, and finally a mix. Eight questions per page with tick boxes and its own separate answer key.
Common questions
- Is √2 + √3 equal to √5?
- No. Unlike surds combine no more than x and y do. Nothing on this worksheet models that error.
- Are any answers given as decimals?
- No. Every answer is exact — a coefficient and a square-free radicand.
- How is exactly one option guaranteed correct?
- Options are compared in canonical surd form, so a distractor cannot accidentally equal the answer.
- Is an answer key included?
- Yes. Every level downloads with a key giving the letter and the exact surd.
A hand for grown-ups
- Before you start
- Find a calm few minutes with no rush. Let your child know it is fine to find some of it tricky — that is what practice is for.
- While they work
- Sit nearby but let them lead. If they get stuck, ask "what could you try?" rather than giving the answer — the thinking is the point.
- Afterwards
- Ask them to show you one they found easy and one they found hard. Praise the effort on the hard one, not just the right answers.
- Watch out for
- Rushing. If answers come too fast and wrong, slow the pace down together rather than pushing for more.
- Away from the screen
- Look for the same maths in everyday life — counting stairs, sharing snacks, spotting shapes on a walk.
Where to go next
Chosen by the skills this activity practises.