Square of a Number

Introduction

Calculating the square of a two-digit number can be made easier using specific techniques. Let’s explore how to calculate the square of numbers ending in 5 and other numbers.

Number Ending in 5

When dealing with numbers ending in 5 (e.g., 25, 35), follow these steps:

Step 1:

Multiply the first digit of the number by the next consecutive number.

Example: For 25, 2 x 3 = 6.

Step 2:

Add 25 to the end of the result obtained in Step 1.

Example: (6)(25) = 625

Other Numbers

For numbers not ending in 5 (e.g., 24, 36), the process is slightly different:

Step 1:

Identify the nearest multiple of 10 to the number.

Example: For 24, the nearest multiple of 10 is 20, and for 36, it is 40.

Step 2:

Calculate the absolute difference between the nearest multiple of 10 and the number.

Example: For 24, |20 - 24| = 4, and for 36, |40 - 36| = 4.

Step 3:

Adjust the number to be squared based on the comparison with the nearest multiple of 10.

Example: For 24, since 20 < 24, 24 + 4 = 28; for 36, since 40 >= 36, 36 - 4 = 32.

Step 4:

Mentally multiply the adjusted number with the nearest multiple of 10 to get Result1.

Example: For 24, Result1 = 28 * 20 = 560; for 36, Result1 = 32 * 40 = 1280.

Step 5:

Square the absolute difference calculated in Step 2 to get Result2.

Example: For 24, Result2 = 4 * 4 = 16; for 36, Result2 = 4 * 4 = 16.

Step 6:

The final result is the sum of Result1 and Result2.

Example: For 24, Result = 560 + 16 = 576; for 36, Result = 1280 + 16 = 1296.

Once you have mastered this technique, feel free to share it with your friends and help them out as well.