In SSC CGL Tier 1 and Tier 2, Quantitative Aptitude rewards speed as much as accuracy. Candidates who memorize squares, cubes, and a handful of algebra shortcuts routinely save 15–20 minutes per paper — time that can be redirected to tricky DI and geometry questions. Below are the exact shortcut methods and memory charts every serious SSC CGL aspirant should have on their wall.
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1. Why Squares & Cubes Memorization Is a Game-Changer
Roots, ratios, mensuration, and algebra questions in SSC CGL frequently require instant recall of squares and cubes. Instead of calculating on the spot, toppers memorize the full chart from 1 to 40 so recognition becomes automatic — this alone is one of the biggest speed gains available in the Quant section.
Squares & Cubes Memory Chart — Numbers 1 to 20 (with fast square root shortcut)
Squares & Cubes Memory Chart — Numbers 21 to 40
Fast Square Root Trick
To find √7744: the last digit is 4, so the root must end in 2 or 8. It lies between 80² (6400) and 90² (8100), and 7744 is closer to 8100 — so the answer is 88. This last-digit-plus-range logic narrows down any 4-digit perfect square in seconds.
2. Multiplication Shortcuts That Save Real Exam Time
Beyond squares and cubes, a small set of multiplication tricks handles a large share of SSC CGL arithmetic and simplification questions without a single line of long multiplication.
Speed Maths Shortcuts — Multiply by 999, Multiply by 11, Criss-Cross Method & Algebra Identities
- Multiply by 999: 654 × 999 = (654 − 1) joined with (each digit of 653 subtracted from 9) → 653346.
- Multiply by 11: 43 × 11 → keep the last digit (3), add the two digits (4+3=7), keep the first digit (4) → 473.
- Criss-Cross (2-digit × 2-digit): 23 × 12 → ones: 3×2=6, cross: (2×2)+(3×1)=7, tens: 2×1=2 → 276.
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3. Must-Know Algebra Identities for SSC CGL
Algebra questions in both Tier 1 and Tier 2 are almost entirely identity-based. Memorizing the following identities cold means you can solve most algebra questions in under 20 seconds:
| Identity | Name |
|---|---|
| (a+b)² = a²+2ab+b² | Square of sum |
| (a-b)² = a²-2ab+b² | Square of difference |
| a²-b² = (a+b)(a-b) | Difference of squares |
| (a+b)³ = a³+3a²b+3ab²+b³ | Cube of sum |
| a³+b³ = (a+b)(a²-ab+b²) | Sum of cubes |
| a³-b³ = (a-b)(a²+ab+b²) | Difference of cubes |
| (a+b+c)² = a²+b²+c²+2ab+2bc+2ca | Square of trinomial |
| if a+b+c=0 → a³+b³+c³=3abc | Special case |
4. How to Use These Charts in Daily Practice
- Daily recall drill: Cover the square/cube columns and test yourself for 5 minutes every morning until recall is instant.
- Apply, don't just memorize: Use the multiply-by-11, multiply-by-999, and criss-cross tricks while solving previous year papers so they become muscle memory under timed conditions.
- Identity flashcards: Write each algebra identity on a flashcard and shuffle-test yourself weekly — SSC CGL algebra questions are almost always a direct or disguised application of these identities.
Pro Topper Tip
Print all three charts and stick them where you'll see them daily — beside your study desk or as your phone lock screen. Passive repeated exposure combined with active recall drills is the fastest way to make squares, cubes, and identities permanent.
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Frequently Asked Questions (FAQs)
Why should I memorize squares and cubes up to 40 for SSC CGL?
Instant recall of squares and cubes removes an entire calculation step from roots, ratios, mensuration, and algebra questions, making it one of the single biggest speed gains available in SSC CGL Quant.
What is the fastest way to find the square root of a 4-digit perfect square?
Check the last digit to narrow down the possible ending digits of the root, then identify which two consecutive multiples of 10 the number falls between, and pick the one it is closer to. This narrows any 4-digit perfect square to its root in seconds.
How does the multiply-by-11 shortcut work?
For a 2-digit number, keep the last digit as is, add the two digits together for the middle digit, and keep the first digit as is. For example, 43 × 11 becomes 4, (4+3), 3 → 473.
How do I multiply a number by 999 quickly?
Subtract 1 from the original number for the first part of the answer, then subtract each digit of that result from 9 for the second part, and join the two. For example, 654 × 999 → (654−1) joined with (9-minus-each-digit of 653) → 653346.
What is the criss-cross method used for?
The criss-cross method is a shortcut for multiplying two 2-digit numbers without long multiplication. You multiply the ones digits, cross-multiply and add for the middle term, then multiply the tens digits, combining all three to get the answer instantly.
Which algebra identities are most important for SSC CGL?
The square of sum, square of difference, difference of squares, cube of sum, sum of cubes, difference of cubes, square of a trinomial, and the special case where a+b+c=0 gives a³+b³+c³=3abc are the identities asked most frequently in SSC CGL algebra questions.
How often should I practice these shortcuts to make them exam-ready?
Practice the squares and cubes chart daily until recall is automatic, and apply the multiplication tricks and algebra identities while solving previous year papers so they become muscle memory under timed conditions rather than something you have to consciously recall.