Whether you are a student, teacher, engineer or anyone who often confronts numbers, you would agree that squaring numbers can be a tedious task - especially when handling large numbers or working without a calculator. But here's a surprise: There is a simple trick to square numbers ending in 5, and nailing this technique will make you more efficient and competent in dealing with numbers. Let's dissect this beautiful method of mathematics!
In this trick, for squaring any number that ends in 5, you separate the number into two parts: the last digit (which is always 5) and the digits before 5. After that, multiply the digits (except 5) by the number one greater than itself and then attach 25 (the square of 5) to the end of the result. This is possible because, mathematically, (10n+5)^2 = 100n*(n+1) + 25 where n is the number other than the last 5 in the number that to be squared. This is quite similar to the formula (a+b)^2 where we calculate the squares of both terms and also the product, but in a more simplified manner.
Let's demonstrate with some examples:
Example 1: Consider 15^2. Here, the number before 5 is 1. Now, multiply 1 by the number greater than it, which is 2. This gives us 2. Attach 25 to the end of the result and you end up with 225, which is indeed the square of 15.
Example 2: Now look at 25^2. The number before 5 is 2. Multiply 2 by the next number, i.e., 3, which equals 6. Now attach 25 to the result and you get 625 - the square of 25.
Example 3: Let's take a look at 35^2. The number before 5 is 3. Multiply 3 by the next number, 4, which gives us 12. Now attach 25 at the end and you have 1225 - the square of 35.
Example 4: Consider a larger number, 105^2. Here, the numbers before 5 are 10. Multiply 10 by the next number, 11, gives you 110. Attach 25 to the end and you get 11025, which is indeed the square of 105.
This technique works not only for two or three-digit numbers, but for any number ending in 5. So there you have it! You can now square any number ending in 5 with relative ease!