SSC CGL Square and Cube Root Practice Test 2026 — Free Chapter Wise Questions

Square & Cube Root Tests — Pick a Level and Start

Tap a level to see every test in it. Start at Level 1 the day you finish the digit tricks, then move to Level 2 with the timer running to push accuracy under pressure.

Square and cube root is the fastest scoring chapter in SSC CGL Quantitative Aptitude, and the one where the gap between a prepared and an unprepared candidate is most visible. Someone who knows the digit tricks reads √4489 in about six seconds; someone who reaches for long division spends ninety and can still slip. Nearly every shift carries a question that belongs to this chapter outright — a direct root, a least number to add or subtract, or a counting question — and the same skills decide how quickly you move through simplification, surds and indices, and mensuration.

These practice tests put twenty-five such questions in front of you in one sitting, which is what turns the last-digit table from something you can recite into something you apply without thinking. Every question comes with a full solution and the shortcut, in English or Hindi.

How Many Square and Cube Root Questions Are Asked in SSC CGL?

The chapter usually gets one to two direct questions, and its methods are reused inside simplification, surds and indices, and anywhere a root has to be taken at speed.

Typical spread across recent SSC CGL shifts. SSC does not publish a chapter-wise breakup, so treat these as planning ranges. Tier I maths is always 25 questions in a locked 15-minute section.

What You Will Practice in the Square & Cube Root Chapter

Core topics

• Square roots of four-, five- and eight-digit perfect squares by the last-digit and decade method
• Square roots of decimals, fractions, mixed numbers and powers of ten
• Repeating-digit patterns — 11² = 121, 111² = 12321, 3333² = 11108889
• The identities n² + n + (n + 1) = (n + 1)², n(n + 2) + 1 = (n + 1)² and a² − b² = (a + b)(a − b)
• Digit-count rules for square roots and cube roots, forwards and backwards
• Cubes and cube roots — negatives, decimals, fractions and mixed expressions
• Chains of cube roots, mixed-index radicals and radicals written as fractional powers
• The missing digit that makes a number a perfect square or cube
• Least number to add, subtract, multiply or divide to reach a perfect square or cube
• Greatest and least n-digit perfect squares and cubes
• Counting problems — squares in a range, naturals between consecutive squares, non-squares, sixth powers, and integers trapped between radical bounds
• Word problems that reduce to a square — equal contributions, rupees and paise, rows and columns, and arrangements with a remainder

Squares you should know on sight

Keep the round anchors with them — 40² = 1600, 50² = 2500, 60² = 3600, 70² = 4900, 80² = 6400, 90² = 8100 — because those place a root inside the right decade.

The last-digit rule for squares

Every ending comes from a pair of digits, so the last digit narrows the root to two candidates and the decade picks between them. A number ending in 2, 3, 7 or 8 is never a perfect square; a square ending in 5 must end in 25; and a perfect square always ends in an even number of zeros.

Cubes, and why cube roots are easier

The last digit of a cube identifies the last digit of its root uniquely — only 2, 3, 7 and 8 swap places, and the rest map to themselves. So for any perfect cube up to six digits: strike off the last three digits and the block that remains sits between two cubes, whose smaller root is the ten digit; the last digit of the number then gives the unit digit. ∛262144 → 262 lies between 216 and 343, so the ten digit is 6, and the number ends in 4, so the root is 64.

Decimals, and the one rule that covers them

The digits of the root never change — only the point moves. Given √0.5776 = 0.76, it follows at once that √57.76 = 7.6 and √0.005776 = 0.076, with no fresh working.

Add, subtract, multiply or divide — the four cousins

The add and subtract answers always sum to (k + 1)² − k² = 2k + 1, which makes a quick check. Cubes use the same layout with k³ and (k + 1)³.

Also worth memorising

• A number with 2n or 2n − 1 digits has a square root with n digits; group in threes from the right for cube roots
• Exactly 2n natural numbers lie between n² and (n + 1)², and none of them is a square
• Both a perfect square and a perfect cube means a sixth power k⁶ — 1, 64, 729, 4096, 15625
• (10n + 5)² = n(n + 1) followed by 25 — so 235² = 55225, and read backwards, √55225 = 235
• Greatest 2n-digit perfect square has a root made of n nines: 999² = 998001
• a < √N < b means a² < N < b²; a < ∛N < b means a³ < N < b³
• ∛(−a) = −∛a — a cube root keeps the sign, a square root does not

Square & Cube Root Chapter Notes

Every rule on this page is worked out in full in the chapter notes — the digit tables, the decimal-point rules, the four add-subtract-multiply-divide types, the counting shortcuts and the traps that cost marks, with examples throughout. Read the notes first if the chapter is new to you, then come back and attempt Level 1.

Solved Examples — SSC CGL Square & Cube Root

How the Square & Cube Root Chapter Tests Work

• 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
• Optional 30-minute timer — with the clock to build exam speed, without it while you are still learning the tricks.
• Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
• Solutions, shortcut tricks and concept notes open after you submit, question by question.
• English and हिंदी, chosen at the start of every test.
• Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.

How to Prepare Square & Cube Root for SSC CGL

1. Learn squares to 30 and cubes to 12 first. Everything in the chapter is built on them, and no trick works without them.
2. Drill the last-digit table until it is reflex. The last digit narrows a square root to two candidates; the decade decides. That is the whole method for four- and five-digit roots.
3. Fix the decimal rule in one line: halve the places for a square root, divide by three for a cube root, by four for a fourth root. Mixing these up shifts the answer by a factor of ten and lands you on a distractor.
4. Never forget the sign on a cube root. ∛(−5832) = −18. This single slip costs more marks in this chapter than anything else.
5. Practise factorisation for the multiply and divide types. Squares need every exponent even; cubes need every exponent to reach a multiple of three.
6. Read the last line of the question again. One stem can contain the number added, the square reached and its root — and only one of them is the answer.
7. Do Level 1 untimed, the same day you finish the tricks. The aim is correct recall, not speed.
8. Move to Level 2 with the 30-minute clock on. Then verify against a previous year paper and a full mock test under locked sectional timing.

Related SSC CGL Maths Chapters

These chapters share methods with squares and cube roots. Practising them together is the fastest route through the arithmetic block.

SSC CGL Square & Cube Root — Frequently Asked Questions

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