 Hello friends so welcome to Centrum Academy and in this particular class as you can see on the board we are going to discuss about one speed math technique which is in extension so to what we discussed in the previous video. So here we would like to discuss squares of the numbers which are based on number 50. So as you remember in the last video we have discussed to find out a square of numbers which are based on number 100. Now when I say as I discussed in the previous video also that when I say based on any particular number then we know that it would be 50 plus x here or 50 minus x here like I as I discussed in the previous video squares of the number based on 100 was nothing but 100 plus something 100 minus something. So I took few examples and you came to know about how to find out square of numbers based on number 100. Now this particular method is also based on the techniques that we have discussed there with few variations here and there. So here I have not written squares of numbers 1 to 25 in the previous video which was the first video on this technique I had written numbers from 1 to 25 square of numbers from 1 to 25 and I hope by now you could have remembered it. If not do remember squares of number 1 to 25 because if you have a habit of just writing squares of number from 1 to 25 without any calculation then these techniques will work out in much better manner. So as we can see here it's what we were doing in the last video was suppose I took a number 112 and if I had to find out 112 square so I defined x as 112 minus 100 and that gave me 12. So I took x square and that gave me 144 and then I took last two digits 44 and so I call it n plus x plus 1 so 112 plus 12 plus 1 so that gives me 125 so I add 125 here so my square was 12544 this I did to show you how the square was found out for number based on 100. Now method to find out squares of numbers based on 50 remains same so suppose I take any number for that matter let me take a number 63. Now here also we would like to find out x what is x? x is difference of number from base as we saw it in the last video. So what is the base here base here is 50 so x would be equal to 63 minus 50 this is the difference of the number from the base that gives me 13. Now we know that we have to find out x square so x square is 169 the last two digits of the x square I will check so for number square I will have last two digits of x square and that gives me 69. Now let me discuss about the difference here from the 100 base so the difference here is in 100 base we do n plus x plus the carryover this is in 100 base what do we do in 50 base? In 50 base number does not matter in base 50 for all the squares that we take on base 50 the number will not matter. So what will matter in place of n what should be written in place of n or what should replace n so as the number does not matter here n is replaced by 25 so this is nothing but 25 plus x plus carryover so for all the numbers take any number on 50 base there it is for rest of the numbers it is 25 plus x plus carryover. So for here in case of 63 I have 25 x is 13 and the carryover here is 1 so I will write 25 plus 13 plus 1 that gives me 39 so n square would be equal to 3969 so 63 square from my calculation here with this technique comes out to be 3969 if you will do it in your calculator or do it with the normal way you will find that this is the answer that you get. Let me take one more example so let's take I take 74 square so here x comes out to be 74 minus 50 so x is equal to 24 so x square is equal to 576 I take last two digits so for n square last two digits would be last two digits of x square which is 76 and carryover from here comes out to be 5 now the rest of the digits would be this would be 25 plus x plus carryover always remember for any number this is 25 so this gives me 25 plus 24 plus carryover is 5 so this gives me nothing but 54 so answer comes out to be 5476 so n square is nothing but 5476 okay now let me take a number which is lesser than 50 and let me show you how to find out a square of that number let me take a number suppose 43 so if I have to find out 43 square so x here would be equal to 43 minus 50 which gives me minus 7 x square comes out to be equal to 49 so for number square because whether it is positive or negative square will always be positive last two digits is how much 49 and what about rest of the digits so I know that this is 25 plus x but x here is what negative so a resultant is 25 minus 7 and that gives me 18 so this comes out to be 1849 so number square is nothing but 1849 and this negative this subtraction happened because here the number for which I have to find out square is lesser than 50 hence the difference would be negative so when I do 25 plus x that is in principle nothing but subtraction so because x is negative so I do 25 minus 7 and that gives me 18 hence the square comes out to be 1849 let me take one more square where we get carryover in case of finding out x square so if I take 31 square for that matter so for 31 square x is equal to 31 minus 50 and that gives me minus 19 so x square is equal to 361 now last two digits here is 61 so n square is equal to last two digits I write 61 my carryover is 3 so carryover is 3 here now this I know as 25 plus x plus carryover so I know that because the value of x is negative so I write 25 minus 19 plus 3 is equal to 9 so this gives me 961 so n square comes out to be equal to 961 and you should always remember that whether you do plus x or minus x carryover will always be added this point I emphasized on in the last video also in which we discussed the squares of number based on 100 and this particular point I am emphasizing here also you should not get confused between value of x and value of carryover whether you do 25 plus x or minus x as we are doing here 25 minus 19 carryover will always get added so I have seen these mistakes being made by a few students so I am emphasizing on this point that whenever you have carryover you always add that carryover carryover whether in case of number more than base or less than base whether we do 25 plus x minus x n plus x n minus x in place of 100 base we will always add carryover so that's it in this particular video I hope you understood the concept this kind of speed matrix do help in regular calculations and increase our calculation efficiency so I hope you understood the concept and you like the videos thank you so much for watching this video and wish you all the best from Centrum Academy thank you