Squares, Cubes, Square Roots and Cube Roots
Squares, Cubes, Square Roots and Cube Roots
Half of your simplification speed comes from numbers you should never calculate — you should simply recall them. Squares up to 30, cubes up to 15, and the roots of common perfect squares must be instant. Every second spent working out 17² by hand is a second stolen from a harder question elsewhere, and over a 20-minute section those seconds decide whether you finish.
What to Memorise
Build recall of the four groups below until each answer arrives before you have finished reading the number. This is rote work, but it is the highest-value rote work in bank quant because these values reappear inside simplification, number series and quadratic equations alike.
- Squares 1–30 — know 25² = 625, 24² = 576 and 19² = 361 cold
- Cubes 1–15 — 12³ = 1728, 13³ = 2197, 14³ = 2744
- Square roots of perfect squares up to 900
- Cube roots of perfect cubes up to 3375
Shortcut: Squares of Numbers Ending in 5
(n5)² = n × (n+1), then write 25
For 35²: n = 3, so 3 × 4 = 12 and you append 25 to get 1225. For 85²: 8 × 9 = 72, append 25 → 7225. This works for every number ending in 5 and is far quicker than long multiplication, which is exactly why it appears so often in speed-based DI cells.
Shortcut: Cube Root of a Perfect Cube by Last Digit
The unit digit of a cube fixes the unit digit of its root. A cube ending in 8 has a root ending in 2; ending in 7 gives 3; ending in 2 gives 8; ending in 3 gives 7; all other endings match themselves. For ∛2744 the last digit 4 means the root ends in 4; ignore the last three digits, and since 2 lies between 1³ and 2³ you take 1, giving 14.
| Cube ends in | Root ends in |
|---|---|
| 0, 1, 4, 5, 6, 9 | same digit |
| 2 | 8 |
| 8 | 2 |
| 3 | 7 |
| 7 | 3 |
Solved Examples
Example 1: 45² = 4 × 5 = 20, then append 25 → 2025.
Example 2: ∛4913. Last digit 3 means the root ends in 7; 4 lies between 1³ and 2³ so take 1 → 17.
Example 3: √5476. It ends in 6, so the root ends in 4 or 6; testing, 74² = 5476, so the answer is 74 — found without any long division.
✗ Long division to find √5476 | ✓ Unit-digit method: ends in 6, and 74² = 5476
Estimating Roots of Non-Perfect Squares
Sometimes a number is not a perfect square, and you only need an approximate root — common inside approximation questions. Anchor between the two nearest perfect squares. For √632, note 25² = 625 and 26² = 676, so the answer is just above 25, roughly 25.1. For √150, since 12² = 144 and 13² = 169, the root is a little over 12, about 12.2. This bracketing is enough for any approximation option and takes only a couple of seconds once your squares up to 30 are memorised.
5 पर समाप्त संख्या का वर्ग: n×(n+1) के बाद 25 लगाएँ। घनमूल में इकाई अंक से मूल का इकाई अंक तय होता है — यह याद रखना बहुत समय बचाता है।
Exam Pointer — SBI Clerk rarely asks a standalone square-root question, but these values sit inside simplification, number series and quadratic equations. Weak recall here slows down three different question types at once, which is why building this table into reflex is one of the highest-leverage things you can revise the night before the exam.
60-Second Recap
- Memorise squares to 30 and cubes to 15 — recall, never compute.
- (n5)² = n(n+1) then 25.
- Cube root: unit digit gives the root's unit digit; the leading group gives the tens.
- Speeds up simplification, series and quadratics together.