Speed maths / Vedic maths - Part 2 (Square of a number)

  Hi people.

Welcome to the second part of the speed mathematics. 

Now let's learn the tricks to solve the squares in this article.

First trick is one's digit with number 5.

Section I : 

Consider this example. 

45 * 45 = 2025

Initially if the number is in terms of 5 then multiply 5 * 5 and put 25.

Then, take the next number of  the ten's digit i.e. 3. Multiple 4 * 5 = 20.

Then concatenation of those numbers gives 2025.

This is the first basic trick to know about while learning squares. This is a simple mind calculation.

Question no 1 : 65 * 65

Question no 2 : 35 * 35 

Question no 3 : 85 * 85 

Make a note that squaring a two digit number will certainly give us a four digit number.

Section II : 

Now let's learn the simplest trick to calculate the squares.

It is tedious, difficult and time consuming to solve by the squares of any number by traditional method.

But now let's do a mind calculation by taking base of the square of that number accordingly.

Take any number to square it.

Consider this one 48.

Squaring the number 48 => 48 * 48.

The first step is to take the base.

Take 50 as a base for the numbers from 1 to 100.

Divide the base by 2 we get 25. 

The second step is to calculate in our mind for finding the squares.

Here 50 - 2 gives 48. So take (-2)^2 which gives 04.

The third step is to add the number with 25.

So adding 25 + (-2) gives 25 - 2 that is equal to 23.

Hence we found the answer i.e. 2304.

Let's have a closer look on the other examples.

Take a number 58.

To square it, we have to follow three steps.

Now the first step is taking the base.

As 58 is a nearby number to 50.

So I consider 50 as a base. We will divide 50 by 2 which gives 25.

Now let's go for the second step.

Here it's 50 + 8 so take (+8)^2 which gives us 64. So put this number at one end in our mind.

Then go for the third step where 25 + 8 gives us 33.

So the answer is 3364.

I hope this clarifies.

Follow these 3 steps for calculating any kind of numbers from 1 to 100.

To calculate the squares of numbers greater than 100 we have to take the base accordingly to find the answer.

Section III : 

Now consider this number 78.

If we take 50 as a base it's 50 + 28 

So take 25 by dividing 50/2.

Then calculate the square of (+28)^2 = 784.

Then the third step is to sum up 25 and 28 which gives 53.

Hold a second now squaring of two digit number will give us a four digit number right.

Here, the number we get 784 by squaring 28 right in that 7 is a carry.

So simply add 53 + 7 in simple way we can say like 25 + 28 + (carry if any).

Therefore we get 25 + 28 + 7 = 60.

Concatenation of those numbers are 6084 which is an answer.

Section IV : 

Now let's use this trick to calculate the numbers nearby to 100.

Take out this number 98.

We can square this number in 3 seconds.

Taking 100 as a base 100 -2 is 98. So we put (-2) * ( -2) which will give us 04.

Put that number aside.

Then calculate 98 - 2 which gives 96.

I hope this clarifies the square of a number.

Questions :

1) 69 * 69

2) 102 * 102

3) 88 * 88

4) 49 * 49

5) 75 * 75

Kindly try the questions given above and post your comments and doubts in the comments section.