Quick Trick to Find Squares of Numbers Near 10, 100, 1000

Introduction

Squaring numbers can often feel like a tedious task, but with the right techniques, you can calculate squares of numbers near 10, 100, or 1000 in seconds. These simple mental math tricks will save you time in competitive exams and daily calculations.

Squaring Numbers Close to 10

Numbers close to 10, such as 9 or 11, can be squared using a simple formula:

Formula:

[ (10 + x)^2 = 100 + 20x + x^2 ]
[ (10 – x)^2 = 100 – 20x + x^2 ]

Examples:

1. 9²
   [ 9 = (10 – 1) ]
   [ 9² = 100 – 20(1) + 1² = 81 ]
2. 11²
   [ 11 = (10 + 1) ]
   [ 11² = 100 + 20(1) + 1² = 121 ]

Squaring Numbers Close to 100

For numbers near 100, we use a similar approach:

Formula:

[ (100 + x)^2 = 10000 + 200x + x^2 ]
[ (100 – x)^2 = 10000 – 200x + x^2 ]

Examples:

1. 98²
   [ 98 = (100 – 2) ]
   [ 98² = 10000 – 200(2) + 2² = 9604 ]
2. 105²
   [ 105 = (100 + 5) ]
   [ 105² = 10000 + 200(5) + 5² = 11025 ]

Squaring Numbers Close to 1000

When squaring numbers near 1000, the process remains the same but scales up:

Formula:
[ (1000 + x)^2 = 1000000 + 2000x + x^2 ]
[ (1000 – x)^2 = 1000000 – 2000x + x^2 ]

Examples:

1. 997²
   [ 997 = (1000 – 3) ]
   [ 997² = 1000000 – 2000(3) + 3² = 994009 ]
2. 1003²
   [ 1003 = (1000 + 3) ]
   [ 1003² = 1000000 + 2000(3) + 3² = 1006009 ]

Why These Tricks Matter

• Speed up calculations: Ideal for competitive exams like GRE, GMAT, and CAT.
• Enhance mental math skills: Avoid unnecessary dependency on calculators.
• Easy to learn and apply: With minimal practice, these become second nature.

Conclusion

Mastering these simple squaring tricks will not only make your calculations faster but also boost your confidence in mathematics. Keep practicing, and soon you’ll be able to square numbers mentally in just a few seconds!