Young Geniuses · Ages 13 to 14
Surds and Indices Fill-in
Simplify surds and apply the laws of indices. A Grade 8–9 algebra worksheet with five levels and 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 Surds and Indices Fill-in
Surds and Indices Fill-in gives upper-secondary learners focused practice with two closely linked topics: simplifying surds and applying the laws of indices. Each question asks the student either to write a square root in its simplest surd form, such as simplifying the root of twelve to two root three, to multiply surds together, or to combine powers of the same base using the index laws. Working confidently with surds and indices is a core expectation of the Grade 8 to 9 number and algebra strands across the US, UK, Canada and Australia, and it is essential groundwork for standard form, quadratic equations and later work with irrational numbers. Surd simplification rests on spotting the largest square factor inside the root, while the index laws turn repeated multiplication and division into simple addition and subtraction of exponents — two ideas these questions rehearse directly. Because the numbers and powers change every time, the worksheet stays fresh and reusable, and the five levels grow the size of the values. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own complete answer key giving the simplest form for each question. There is no advertising, no sign-up and no data leaves the device.
Common questions
- What is a surd?
- A root, such as √12, that cannot be simplified to a whole number — here written in simplest form.
- What grade is this for?
- Grade 8 to Grade 9 learners aged 13 to 14.
- Is an answer key included?
- Yes, every level gives the simplest form for each question.
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.