Shortcut Trick to Find the Cube of a Number Between 1 and 100 in 10 Seconds

Shortcut Trick to Find the Cube of a Number Between 1 and 100 in 10 Seconds

Quick Trick: Calculate Cubes of Numbers 1-100 in Seconds

Method 1: Shortcut for Finding the Cube of a Number (1 to 50)

For numbers between 1 and 50, we use the binomial expansion formula:(B+x)3=B3+3B2x+3Bx2+x3(B + x)^3 = B^3 + 3B^2x + 3Bx^2 + x^3(B+x)3=B3+3B2x+3Bx2+x3

where:

  • B is the nearest multiple of 10
  • x is the difference between the number and B

Example 1: Find 23³

  1. Nearest base (B) = 20, so x = 3
  2. Apply the formula: (20+3)3=203+3(202)(3)+3(20)(32)+33(20 + 3)^3 = 20^3 + 3(20^2)(3) + 3(20)(3^2) + 3^3(20+3)3=203+3(202)(3)+3(20)(32)+33
  3. Calculate step-by-step:
    • 203=800020^3 = 8000203=8000
    • 3(400)(3)=36003(400)(3) = 36003(400)(3)=3600
    • 3(20)(9)=5403(20)(9) = 5403(20)(9)=540
    • 33=273^3 = 2733=27
  4. Final Sum: 8000+3600+540+27=121678000 + 3600 + 540 + 27 = 121678000+3600+540+27=12167

✔️ Answer: 23³ = 12,167

Example 2: Find 47³

  1. Base (B) = 50, so x = -3
  2. Apply the formula: (50−3)3=503−3(502)(3)+3(50)(32)−33(50 – 3)^3 = 50^3 – 3(50^2)(3) + 3(50)(3^2) – 3^3(50−3)3=503−3(502)(3)+3(50)(32)−33
  3. Calculate step-by-step:
    • 503=12500050^3 = 125000503=125000
    • 3(2500)(3)=225003(2500)(3) = 225003(2500)(3)=22500
    • 3(50)(9)=13503(50)(9) = 13503(50)(9)=1350
    • 33=273^3 = 2733=27
  4. Final Sum: 125000−22500+1350−27=103823125000 – 22500 + 1350 – 27 = 103823125000−22500+1350−27=103823

✔️ Answer: 47³ = 103,823

Method 2: Shortcut for Finding the Cube of a Number (51 to 100)

For numbers above 50, we use the formula:(100−x)3=1003−3(1002)x+3(100)x2−x3(100 – x)^3 = 100^3 – 3(100^2)x + 3(100)x^2 – x^3(100−x)3=1003−3(1002)x+3(100)x2−x3

Example 3: Find 97³

  1. Base (B) = 100, so x = 3
  2. Apply the formula: (100−3)3=1003−3(1002)(3)+3(100)(32)−33(100 – 3)^3 = 100^3 – 3(100^2)(3) + 3(100)(3^2) – 3^3(100−3)3=1003−3(1002)(3)+3(100)(32)−33
  3. Calculate step-by-step:
    • 1003=1000000100^3 = 10000001003=1000000
    • 3(10000)(3)=900003(10000)(3) = 900003(10000)(3)=90000
    • 3(100)(9)=27003(100)(9) = 27003(100)(9)=2700
    • 33=273^3 = 2733=27
  4. Final Sum: 1000000−90000+2700−27=9126731000000 – 90000 + 2700 – 27 = 9126731000000−90000+2700−27=912673

✔️ Answer: 97³ = 912,673

Example 4: Find 88³

  1. Base (B) = 100, so x = 12
  2. Apply the formula: (100−12)3=1003−3(1002)(12)+3(100)(122)−123(100 – 12)^3 = 100^3 – 3(100^2)(12) + 3(100)(12^2) – 12^3(100−12)3=1003−3(1002)(12)+3(100)(122)−123
  3. Calculate step-by-step:
    • 1003=1000000100^3 = 10000001003=1000000
    • 3(10000)(12)=3600003(10000)(12) = 3600003(10000)(12)=360000
    • 3(100)(144)=432003(100)(144) = 432003(100)(144)=43200
    • 123=172812^3 = 1728123=1728
  4. Final Sum: 1000000−360000+43200−1728=6834721000000 – 360000 + 43200 – 1728 = 6834721000000−360000+43200−1728=683472

✔️ Answer: 88³ = 683,472

Quick Reference Table for Perfect Cubes (1 to 20)

NN³NN³
1³111³1331
2³812³1728
3³2713³2197
4³6414³2744
5³12515³3375
6³21616³4096
7³34317³4913
8³51218³5832
9³72919³6859
10³100020³8000

Bonus: A Vedic Math Trick for Single-Digit Cubes

For smaller numbers (1 to 9), use this pattern:

  1. Write down four digits in a specific order
  2. Multiply each step using a simple pattern.

Example: Find 9³

  1. Write 9, 81, 729, 729 (each number comes from multiplying 9 in order).
  2. The answer is 729 ✅

Final Thoughts

By using these shortcut tricks, you can calculate any cube between 1 and 100 within 10 seconds! 🔥 Whether you’re preparing for competitive exams, interviews, or quick mental math challenges, this method will save time and effort.

Quick Trick: Calculate Cubes of Numbers 1-100 in Seconds