 Hello friends welcome to Centrum Academy, so we are going to start with videos based on speed map techniques and we will have a series of videos in which we will be discussing different techniques based on speed maps in which we will try to find out squares, cubes, reciprocals and different other techniques related to speed maps, Vedic mathematics also we call it. It was interesting to look at different places where I found that though there are different speed map techniques which has been discussed here and there but there is hardly a place where you will find most of the speed map techniques aggregated at one place. So here we are coming up with a series of videos in which most of the speed map techniques which are required at this level would be available for you which will help you in calculating things faster and if you have these techniques in your hand then you will find that your calculation is becoming faster you will be more accurate and it will help you out at different places. So let me start today with one of the techniques which is very important that is finding out squares of number based on number 100. So let me now take you to the method of finding out squares on the basis of number 100. Before that I have written squares of numbers from 1 to 25. There is a basic reason behind that. So first thing is that to find out squares of number bigger than number 25 we will require squares of number 1 to 25. Why it will be needed because you will see that last two digits of numbers any number more than 25 last two digits of square of that number if I find out m square last two digits of m square would be dependent on last two digits of the squares of any of these numbers depending on what is the relationship between number and one of these numbers. So if you look at the last two digits of this number these numbers you will find that apart from 5, 15 and 25 for which last two digits are 25 for any number ending with 5 last two digits would be 25 otherwise for all other numbers last two digits are different. So if you look at all these numbers last two digits are different apart from 5, 15 and 25 squares. If you take any number more than 25 from 26 to infinite last two digits of square of those numbers would be last two digits of squares of any of these numbers depending on how the relationship is turning out to be between the number for which I am finding out the square and one of these numbers. Now let me take you to actual technique of finding out square. So what do I mean by finding out squares of numbers based on 100? Based on 100 means number something more than 100 or less than 100. Let's see 100 plus x or 100 minus x. How do you find out this x? So suppose I give you a number 107 and is equal to 107. So in this number 107 what is the value of x? X is nothing but how much number is more than 100 or less than 100. So for that I will do x is equal to number minus 100 difference I will find out. So for 107 this difference comes out to be 7. So x comes out to be 7. X is the difference of number and 100 which gives me how much number is more than 100 or less than 100. Why I am finding out x? Because the first step in finding out square of this number, suppose I say n square where n is 107. The first step in finding out n square is to find out x square and x square here is nothing but 49. Now one thing which we have to take care of here is that whenever we are finding out x square we have to only take last two digits. Only last two digits are needed here. So remember that last two digits of number square let me write here last two digits of number square would be equal to last two digits of x square. So what would be last two digits of number square here because last two digits of x square is 49. The last two digits of number square is 49. What about rest of the digits? So for rest of the digits which will come in front of it the method is very simple I do n plus x and in this n plus x what is n? n is the number 107. What is x? x is 7. So 107 plus 7 is equal to 114. So how much it gives me? It gives me 11449. So this is square of 107. Let me take another example. So I am taking an example for number for which x is such that x square is a three digit number. So I have taken 116 here x is equal to 16 so x square is equal to 256. Now here the x square is a three digit number. If I have to take only last two digits what about the third digit here? Just remember that this third digit will go as carry over when I am adding n plus x. So if I have to write n square last two digits of n square would be equal to last two digits of x square which is 56 and then I do n plus x. n plus x gives me 116 plus 16 132 and this two which is not used in x square here will act as carry over here and it will become 134. So I write here 134 square of 116 is 13456. Another example could be 102. Here x is only two and x square is four. Now you can say that it has been told that it has to be a two digit number four is a one digit number. How do you make it a two digit number? So if you look at these squares I have taken these squares only as 010409 why because I have converted these one digit numbers into a two digit numbers from adding zero in front of it. So when you get a one digit number and you have to convert it to a two digit number add zero in front of it. So now your n for n square the last two digits should be 04 and n plus x anyway is 104 so n square comes out to be 1040. So you can see how simple this method is if you practice it with a bit more numbers you will find that the num finding out square for these numbers would be pretty easy. Now let me take a number which is lesser than 100 so n is equal to 92 now what is x here x will be equal to 92 minus 100 minus 8 now x square is how much whether number is positive or negative square will always be positive so x square is 64 so last two digits of number square would be 64 what about rest of the numbers which come in front of it. So I do n plus x here also I do n plus x but the problem is x is negative so it is equivalent to saying that subtract this x from or add this subtract 8 from 92 or add minus 8 to 92 which is like 92 minus 8 gives me 84 so number is 84 or number square is 8464 another number let me take suppose I take 77 x is 23 x square is 529 you can see here I will take only last two digits so last two digits of number square is 29 and n minus x comes out to be 77 minus 23 that gives you 54. Now what about this 5 whether you do n minus x or n plus x this left over digit here will always act as a carryover and carryover is always added so you add 5 here and this will give you 54 plus 559 so you write 5929 as number square so this is how we have to find out the squares of different number based on 100 we first find out x we take x square we take last two digits of x square and then we do n plus x or n minus x depending on number is more than 100 or less than 100 and then if there is a carryover if the square is a 3 digit or a 4 digit or a 5 digit number it can be anything the left over digits would be added to n plus x or n minus x so this is what a clear cut method is by which you can find out squares of these numbers which will help you out in faster calculations and if you practice few more questions maybe 7 8 10 questions you will be thorough in this particular method and probably you will utilize it for your calculation in different subjects in and you will find that this will help you out in increasing the speed of your calculation so thank you so much for watching this video and I hope you understood this particular concept I will be coming up with other video in which I will be discussing squares of numbers based on 50 so till that time I hope you will revise more on this particular concept keep on liking and subscribing us and thank you so much for watching this video thank you