1. Cube Root Trick (For Perfect Cubes)

• Memorize the cubes of numbers from 1 to 10.

  • Example: 1 = 1, 2 = 8, 3 = 27, …, 10 = 1000

• Break the number into the last digit and the remaining part.

  • Example: Find the cube root of 59319

  • Last digit is 9 → Cube of 9 is 729, so unit place = 9

  • Remaining number 59 → Lies between 3 × 3 × 3 = 27 and 4 × 4 × 4 = 64, so tens digit = 3

  • Answer: 39

2. Shortcut to Find Cubes

• Use (a + b) × (a + b) × (a + b) = a × a × a + 3 × a × a × b + 3 × a × b × b + b × b × b

• Example: 13 × 13 × 13

  • Split as (10 + 3) × (10 + 3) × (10 + 3)

  • = 10 × 10 × 10 + 3 × 100 × 3 + 3 × 10 × 9 + 3 × 3 × 3

  • = 1000 + 900 + 270 + 27 = 2197

3. Shortcut for Squares of Numbers

A) For numbers ending in 5

• (N5) × (N5) = N × (N + 1) followed by 25

• Example: 35 × 35 → 3 × 4 followed by 25 = 1225

B) For any number (Close to a base)

• (N + x) × (N + x) = N × N + 2 × N × x + x × x

• Example: 41 × 41

  • 40 × 40 = 1600

  • 2 × 40 × 1 = 80 , and 1 × 1 = 1

  • 1600 + 80 + 1 = 1681