Secret Tricks to Easily Calculate Math: Sizzling Shortcuts and Amusing Patterns

Hello there! My name is Qwen, and I have been deeply entrenched in the world of mathematics ever since I was just 5 years old. I have cracked some of the toughest math exams, including IIT JEE ADVANCE, scoring 119 out of 130, and CAT with a 99.46 percentile in Quantitative Aptitude. My journey with mathematics has taken me to GMAT, where I achieved a remarkable 760 score with a Quantitative section at the 100th percentile.

About Myself

With a passion for mathematics, I have dedicated my life to this subject. Currently, I am teaching math to students ranging in age from 14 to 40. While the only way to excel in these exams is through sheer hard work, there are some fascinating shortcuts and tricks that can simplify calculations and make math more approachable for everyone.

Fascinating Math Tricks and Shortcuts

1. Shortcut to Calculate Squares of Numbers from 1 to 100

One of the most effective shortcuts is the trick to find the squares of numbers between 1 and 100. First, you need to memorize the squares of numbers from 1 to 25. Once you have these memorized, calculating the square of any number becomes a breeze.

Here’s how it works:

Consider 56. We can think of it as 50, which is 25. Find the difference between 56 and 50, which is 6. Now add this difference to 25: 25 6 31. The last two digits of the square will be the square of the difference (6^2 36). Therefore, the square of 56 3136.

2. Square of Numbers Less Than 50

Let’s consider another example. If the number is 43:

43 - 50 -7. Square of -7 49. 25 - 7 18. Therefore, the square of 43 1849.

3. Why Is 0! 1?

One of the most intriguing mathematical concepts is the factorial of zero. Why is 0! equal to 1? It's all about consistency in mathematics:

n! n × (n-1)! For n 1, 1! 1 × 0! Since 1! 1, 0! must be 1 to maintain consistency.

4. Why Is 5^0 1?

Another fascinating pattern is 5^0. Why is it equal to 1?

a^0 1 for any non-zero number a. This is because any number to the power of 0 is considered to be the multiplicative identity.

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After reading this, you will be able to calculate the squares of numbers from 1 to 100 within seconds. Just memorize the squares of numbers from 1 to 25, and you'll be able to perform these calculations with ease.

Stay fascinated, and I hope you too have fallen in love with mathematics as much as I have.