Introduction
Memorising squares and cubes up to 30, combined with two fast manual methods for extracting roots, saves
enormous time on SSC Quant — especially in Mensuration, Algebra, and Trigonometry questions that build on
these values.
Squares Table (1-30) — Memorise This
| n | n² | n | n² | n | n² |
|---|
| 11 | 121 | 18 | 324 | 25 | 625 |
| 12 | 144 | 19 | 361 | 26 | 676 |
| 13 | 169 | 20 | 400 | 27 | 729 |
| 14 | 196 | 21 | 441 | 28 | 784 |
| 15 | 225 | 22 | 484 | 29 | 841 |
| 16 | 256 | 23 | 529 | 30 | 900 |
| 17 | 289 | 24 | 576 | | |
Cubes Table (1-15) — Memorise This
| n | n³ | n | n³ |
|---|
| 1-5 | 1, 8, 27, 64, 125 | 11 | 1331 |
| 6 | 216 | 12 | 1728 |
| 7 | 343 | 13 | 2197 |
| 8 | 512 | 14 | 2744 |
| 9 | 729 | 15 | 3375 |
| 10 | 1000 | | |
Finding Square Root — Unit Digit Shortcut
| Last digit of the number | Possible last digit(s) of its square root |
|---|
| 1 | 1 or 9 |
| 4 | 2 or 8 |
| 9 | 3 or 7 |
| 6 | 4 or 6 |
| 5 | 5 |
| 0 | 0 |
Q. Find √7396 using the shortcut method.
Last digit is 6 → root ends in 4 or 6
Ignore last 2 digits → 73 lies between 8² (64) and 9² (81) → tens digit = 8
Test 84² = 7056 (too small), 86² = 7396 ✓
So √7396 = 86
💡 How the shortcut works: For a perfect square with an even number of digits, find which two consecutive squares the "first part" (all digits except the last two) falls between — that gives the tens digit. Then use the unit-digit table to pick between the two candidate answers.
Cube Root — Unit Digit Shortcut
| Last digit of the number | Last digit of its cube root |
|---|
| 1 | 1 |
| 8 | 2 |
| 7 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 3 | 7 |
| 2 | 8 |
| 9 | 9 |
| 0 | 0 |
⚠️ Note: Unlike square roots, cube root unit digits are unique (no ambiguity) — each last digit maps to exactly one possible cube-root last digit, making this shortcut even faster.
Q. Find the cube root of 205379.
Last digit = 9 → cube root ends in 9
Remove last 3 digits → 205 lies between 5³ (125) and 6³ (216) → take the smaller, 5
So cube root = 59 (verify: 59³ = 205379 ✓)
✅ Practice Focus: Memorise squares (1-30) and cubes (1-15) · Square root unit-digit ambiguity table (two candidates) · Cube root unit-digit table (unique mapping) · Division method for non-perfect squares (used in Mensuration/Trigonometry chapters).