Young Geniuses · Ages 13 to 14
Surds Speed Simplifier
Simplify surds and radicals against a friendly timer in a quantum energy research facility, for ages 13 to 14.
5 levels+40 XP
ProgressNot started
5 levels · BeginnerPlay
Young Geniuses · Ages 13 to 14
All Young Geniuses gamesRationalise Denominator Quiz
Clear the root from the bottom of a fraction: 6 over root 3 becomes 2 root 3. For ages 13 to 14.
QuizRationalise the denominator by clearing a root~9 min per level5 levelsAll devices
- Free · no account required
- COPPA compliant
- +10 XP per level
- 5 levels
- Plays on all devices
- Curriculum-aligned
The learning journey
Every activity is one step. Here is where this one fits.
- Play(you are here)Learn the idea in a game
- PractiseLock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Rationalise Denominator Quiz
Rationalise Denominator Quiz teaches a convention, and it is worth being honest about that from the start. Six over root three and two root three are the same number; neither is more correct than the other, and a student who asks why one of them is not allowed has spotted something real rather than being difficult. The answer is that a root on the bottom of a fraction is awkward to work with and impossible to estimate at a glance, whereas two root three is visibly a little under three and a half. Rationalising is about readability and about making the next step of a calculation possible, not about legality, and saying so tends to produce students who remember the technique rather than resent it. Mechanically it is one move: multiply top and bottom by the root, which turns the bottom into a whole number because a root times itself is the number underneath it. The error that matters comes immediately afterwards. Having multiplied six by root three to get six root three, a great many students stop, when the bottom has also become three and the whole thing simplifies to two root three. Six root three is a properly formed expression that happens to be three times too large, and nothing about it looks wrong. It is offered as an option in every round here for exactly that reason. The first three levels divide exactly; from the fourth the fraction stays, which is the harder written form. Free, no sign-up, no advertising to children.
Where to go next
Chosen by the skills this activity practises.
Next — more of the same skill
Printable worksheets for this skill
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.
How to play
A question appears on screen
A maths question is shown in large text at the centre of the play area. A timer bar begins counting down from 90 seconds.
Choose the correct answer
Answer options are shown as large buttons. Tap an answer, or press keys 1–4 on the keyboard. Any input method works — touch, mouse or keyboard.
Build your streak
Each consecutive correct answer increases your streak. A longer streak lights up the flame icon and adds a bonus multiplier to the XP you earn for the level.
Finish the level
Each level has 6 questions. Complete them to earn the full level reward (+10 XP, plus up to +10 XP for a perfect run). Progress is saved locally and shown on the Parent Dashboard.
Curriculum alignment
Mapped to national curriculum frameworks so teachers and parents can match practice to school standards.
- United StatesCommon Core State Standards for Mathematics · algebra, divisionAligned to algebra, division number and operations objectives.
- United KingdomNational Curriculum for England — Maths · algebra, divisionAligned to algebra, division number and operations objectives.
- AustraliaAustralian Curriculum v9.0 — Mathematics · algebra, divisionAligned to algebra, division number and operations objectives.
- CanadaPan-Canadian Provincial Standards · algebra, divisionAligned to algebra, division number and operations objectives.
Common questions from parents & teachers
Everything you need to know before your child starts playing.
- It is a convention about readability. Both forms are equal, but 2 root 3 is visibly a little under 3.5, while 6 over root 3 tells you almost nothing at a glance.
- Multiply the top and the bottom by the root. A root times itself gives the number underneath, so the bottom becomes a whole number.
- Stopping after multiplying. Six over root three becomes six root three over three, which simplifies to two root three — and six root three looks perfectly well formed.
- No, and our surd simplifier covers that separately. This is specifically about clearing a root from a denominator.
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