# Square Root and Cube Root Questions — Free Practice | ComputePrep > Practise square root and cube root questions free and timed: use the last digit and the nearest known cube to find roots without long division. Worked answers. Source: https://computeprep.com/drill-types/square-root-cube-root --- Squares, cubes & roots # Square root and cube root questions — read the answer off the last digit Square root and cube root questions in exams almost always use perfect squares and cubes, so the answer can be read off rather than computed. The last digit of the number fixes the last digit of the root, and the leading digits fix its size by bracketing between two known squares or cubes. Long division is rarely needed. Squares and cubes are the recall layer underneath half of a quant section: simplification, mensuration, quadratic comparison and most approximation questions all move faster when the first 30 squares and first 15 cubes are instant. This is memory work with a very high rate of return — a few days of drilling pays back across the whole paper. **Try it against the clock.** Squares, Cubes & Roots runs at 15s easy, 20s medium and 30s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading. [Start a timed Squares, Cubes & Roots drill →](https://computeprep.com/?drill=squares_cubes&src=seo-square-root-cube-root) ## How to answer square root and cube root questions by inspection - Use the last digit to fix the root's last digit A perfect square ending in 6 has a root ending in 4 or 6; ending in 9, a root ending in 3 or 7. Cubes are cleaner still — the cube's last digit determines the root's uniquely, and only 2/8 and 3/7 swap places. That single observation removes most of the option list. - Bracket the size with the nearest known square or cube For the square root of 5329: 70² is 4900 and 80² is 6400, so the root is in the seventies, and the trailing 9 makes it 73 or 77. Testing which is a single multiplication. Two steps, no division. - For cubes, strip the last three digits To cube-root 19683, ignore the last three digits: 19 sits between 2³ = 8 and 3³ = 27, so the tens digit of the root is 2. The number ends in 3, so the root ends in 7. The answer is 27, found without any arithmetic beyond recall. - Memorise the base table, then stop calculating Squares to 30, cubes to 15, and the square roots of 2, 3 and 5 to three decimals. Everything above is derived from these in one step, and a candidate who has them does not compute roots at all — they recognise them. ## What the last digit tells you | Number ends in | Its square/cube root ends in | | --- | --- | | Square ends in 1 | Root ends in 1 or 9 | | Square ends in 4 | Root ends in 2 or 8 | | Square ends in 6 | Root ends in 4 or 6 | | Square ends in 9 | Root ends in 3 or 7 | | Cube ends in 2 | Root ends in 8 (and 8 → 2) | | Cube ends in 3 | Root ends in 7 (and 7 → 3) | ## 3 real square root and cube root questions, with worked solutions Generated by the same engine that mints the ComputePrep daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers. ### Question 1 28² = ? Powers and roots — instant recall. - 729 - 784 - 812 - 794 - 841 - Use (a − b)²: (30 − 2)² = 900 − 120 + 4 = 784. ### Question 2 12³ = ? Powers and roots — instant recall. - 1584 - 2197 - 1331 - 1728 - 1872 - 12³ = 12² × 12 = 144 × 12 = 1728. (Exam-standard cube — worth memorising to 15³.) ### Question 3 6³ = ? Powers and roots — instant recall. - 125 - 216 - 343 - 166 - 252 - 6³ = 6² × 6 = 36 × 6 = 216. (Exam-standard cube — worth memorising to 15³.) ## Common mistakes this drill is built from The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks. ### Reaching for long division Exam numbers are perfect squares and cubes by construction. Setting up a division method wastes thirty seconds on a question the last-digit rule answers in five. ### Forgetting that squares have two candidate endings A square ending in 6 could have a root ending in 4 or 6. The bracketing step, not the last digit alone, is what resolves it — skipping it leaves a coin flip. ### Confusing the cube-root digit swap For cubes, 2 and 8 map to each other and so do 3 and 7; every other digit maps to itself. Getting this backwards is the only real trap in cube roots. ## FAQ ### How do I find a square root quickly without long division? Use the last digit to narrow the root's final digit to two candidates, then bracket the number between two known squares to fix the tens digit. For 5329: it lies between 70² and 80², and ends in 9, so the root is 73 or 77 — one multiplication decides. The whole process is faster than setting up a division. ### Which squares and cubes should I memorise? Squares up to 30 and cubes up to 15 cover essentially every exam question, along with √2 ≈ 1.414, √3 ≈ 1.732 and √5 ≈ 2.236. This is the highest-return memory work in quant, because these values reappear in simplification, mensuration and approximation. ### How do I find a cube root of a five-digit number? Ignore the last three digits and see which two consecutive cubes the remainder falls between — that gives the tens digit. Then use the original number's last digit to fix the units digit, remembering that 2 and 8 swap and 3 and 7 swap. For 19683: 19 sits between 8 and 27 so the tens digit is 2, and the trailing 3 gives a units digit of 7, making 27. ## Practise the next topic - [All 23 drill types](https://computeprep.com/drill-types) — the full rotation with every published time limit. - [Simplification questions — BODMAS](https://computeprep.com/drill-types/simplification) — simplification questions, timed. - [Percentage questions for bank exam papers](https://computeprep.com/drill-types/percentages) — percentage questions for bank exam, timed. - [Vedic maths shortcuts](https://computeprep.com/vedic-maths) — the seven sutras that make a 15-second answer possible. - [How to improve calculation speed](https://computeprep.com/calculation-speed) — the six-week arc these drills fit into. ComputePrep is free, needs no account, and is not affiliated with IBPS, SBI, SSC, RRB or any exam authority.