Eduqo
Quantitative Aptitude›Ch 1: Arithmetic Foundations›Squares, Cubes and Roots
Master rapid squares to 30, cubes to 20, factorisation roots, and digit shortcuts.
Memorising squares up to 30 and cubes up to 20 eliminates calculation bottlenecks. Apply prime factorisation and unit digit checks to find roots instantly in exams.
Memory Hooks
| Number (n) | Square (n²) | Cube (n³) |
|---|---|---|
| 12 | 144 | 1728 |
| 15 | 225 | 3375 |
| 20 | 400 | 8000 |
| 25 | 625 | 15625 |
Square Area
(Side times side)
Side times side
A square plot of side 14m has an area of 196 sq m.
Cube Volume
(Length cubed)
Length cubed
A cubic box of edge 5cm holds 125 cubic cm of water.
Factor Root
(Pair identical factors)
Pair identical factors
Factorise 1764 into prime pairs to find its root 42.
Digit Check
(Check unit endings)
Check unit endings
A number ending in 7 can never be a perfect square.
Assuming √a+b equals √a + √b√a+b cannot be split directly
Square roots do not distribute over addition. Always add terms inside the radical first.
Confusing square root sign with plus-minusPrincipal square root is positive
The radical sign √9 strictly means +3, whereas x² = 9 gives both +3 and -3.
Guessing roots by unit digit aloneCheck tens digit and ranges
Multiple numbers can share the same unit digit when squared. Always estimate range first.
Q1.What is the value of √(10 + √(25 + √1089))?
Q2.Evaluate the cube root of 17576 using unit digit and range estimation.