Shortcut method of finding cube of a number within a few seconds

How to Find the Cube of a Two-Digit or Three-Digit Number in Seconds

Finding the cube of a two-digit or three-digit number quickly can be a valuable skill, especially in competitive exams and everyday calculations. Instead of multiplying the number three times manually, you can use simple tricks to get the result in a matter of seconds. In this article, we’ll explain the steps to cube a number and provide examples to make the process easy to understand and implement.

Why Learn How to Cube Quickly?

• Saves time in exams and interviews.
• Helps with mental math and improves calculation speed.
• Enhances precision in handling complex number operations.

Method 1: Cubing a Number Close to a Base (e.g., 100, 50, 1000)

This trick works well when the number you want to cube is near a round base like 100, 50, or 1000. By leveraging the formula for cubes, you can compute the cube easily without much effort.

98 is close to 100. Use the formula for cubing numbers close to a base:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, a = 100 and b = -2. So:

98³ = (100 - 2)³ = 100³ - 3 × 100² × 2 + 3 × 100 × (-2)² + (-2)³

= 1000000 - 60000 + 1200 - 8 = 940192

Method 2: Cubing Any Two-Digit Number Quickly

If the number is not close to a round base, you can apply a more general approach, where you multiply the number by itself three times.

To find the cube of 19, you can follow the straightforward multiplication:

23³ = 19 × 19 × 19 = 361 × 19 = 6859

Trick 3: Cubing a Three-Digit Number

For three-digit numbers, you can still apply the same logic, but you might need to break it down into manageable steps to speed up the process. If the number is near a base (like 100, 200, etc.), use the expansion formula from Trick 1 to get the result quickly.

102 is close to 100. Using the same cube expansion formula:

(100 + 2)³ = 100³ + 3 × 100² × 2 + 3 × 100 × 2² + 2³

= 1000000 + 60000 + 1200 + 8 = 1061208

Tips for Speed and Accuracy:

• Practice cubing numbers close to round bases (like 100, 50, or 1000) to get faster at using the expansion formula.
• Commit the cubes of numbers from 1 to 20 to memory for faster mental calculations.
• Break down larger numbers into smaller chunks, especially when working with three-digit numbers.
• Use a calculator for larger numbers but practice these tricks for mental math and faster calculations.

Conclusion

By using these tricks, you can find the cube of any two-digit or three-digit number in seconds. With regular practice, this method will become second nature, and you’ll be able to solve cubing problems quickly, making you more efficient in exams or real-life applications.