FUN WITH MATHS - 1. The Joy of Squaring

 Finding out the square of a number, that too if it exceeds two digits is often a tedious task. However, we do not need to worry if the number, containing any number of digits ends with a 5.

Here is the reason:

There is a trick mentioned in the first sutra of Vedic maths – ‘Ekādhikena Pūrveṇa’ which means ‘one more than the previous one.’

It has many applications, but a very useful one is squaring numbers ending in 5. 

Till we reach the end of this blog, we shall also derive some other logics using the same trick. Let us take the example – 15 as we know, its square is 225. We shall solve it using the trick.

 

Just combine them without addition, or any other operation.

Therefore,(15)²=225

In the same way, we can say that,

25²=625,                     35²=1225 etc.

Hence, the rule is to simply multiply the number preceeding 5 with its successor and write 25 (i.e. 5²) after it.

What if, we are to square a three-digit number? Well, we will use the following steps. Remember that 5 will always remain on the right side. For example– 105²

From the knowledge of textbooks, we know that the units digit of the square of any number ending with 5 is always 5 but by applying some logic, and keeping in mind, this trick, we can also predict that the last 2 digits of the square of any number ending with 5 are always 25.

And also, the numbers which end with 65, 95 etc. and not with 25 are never perfect squares!

If we are asked √3025, then we can predict the last digit as 5 and we have to estimate such a digit whose product with its successor yields 30 and it is 5.

Therefore,√3025=55