 hello friends welcome to centrum academy so as you know in this series we are discussing about calculation techniques and we have already discussed about finding out squares so we discussed about finding out the squares on base of number 100 and number 50 in this particular video i'm going to teach you how to find out cubes of two digit numbers and before starting this i would like you to remember cubes of unit i mean single digit numbers so that is from 1 to 10 so i'm writing it here for your knowledge so it will be 1 cube is equal to 1 2 cube is equal to 8 3 cube is equal to 27 4 cube is equal to 64 5 cube would be equal to 125 6 cube would be equal to 216 7 cube is equal to 343 8 cube is equal to 512 9 cube is equal to 729 and 10 cube is equal to 1000 so these 10 cubes you should remember others i'm gonna teach you for any two digit number you can find out the cube of that number with the methods which i'm going to discuss over here till now you might have learnt it or you will see at many a places that generally to find out cubes people use the formula a plus b cube so a plus b cube is nothing but a cube plus 3 a square b plus 3 a b square plus b cube so in this particular method the problem is that suppose let's take 37 cube so you assume this to be a to be 3 and b to be 7 from here and if you start putting numbers it becomes really very confusing so i'm not going to use this particular method in this particular method i'm going to teach you different terms different techniques which will help you in finding out cubes in much efficient manner and which will be better than this in terms of speed in terms of efficiency so in the technique i'm going to discuss we divide number in four different classes so that classification is of four types so first one is numbers starting with one starting with one so it means that numbers from 11 to 19 these would be the numbers starting with one then the second classification is numbers ending with one so it can be 21 31 because i have already taken 11 i'm not putting it here 41 likewise till 91 third one is same numbers for that matter 33 44 55 and likewise and the fourth classification is different numbers so unit digit and tense digit does not match so number can be for that matter 24 or 97 or 56 or something like this so there are four classification of numbers that i have made here and for each of this different classifications i will have different methods so these two would be similar in nature there would be just a little bit of difference so in this particular video i want to discuss these two techniques the first two techniques numbers starting with one and number endings ending with one the other two techniques i will be discussing in uh next video so i'm going to start with numbers starting with one now and then i'm going to discuss this uh with a little bit of difference in the technique so we have numbers starting with one so let's take a number 12 and i have to find out 12 cube now please listen to me very carefully what's the technique it's very very simple so suppose i have number 12 i write the number add as it is one and two and then i take this last digit what is the last digit here 12 so last digit in 12 would be two so uh i take square of two so two square is four and i take cube of two so that is eight what am i doing i'm writing the number as it is i'm taking the last digit here which is two and i'm the next two digits would be square and cube of this number two now think is very very simple what i need to do is leave the last digit and the first digit what you have to do leave the last digit and the first digit so i'm leaving one and eight as it is now find out a double of these middle two numbers so four double of four is two times four is eight and two times two is four now we don't have to do anything write eight as it is add this four plus eight is 12 so what is the carry over one this carry over will go here so one plus two three three plus four is seven no carry over so one come as it is this is the cube of 12 i will again repeat i had 12 so i wrote 12 as it is the last digit is two so i take square of two as four then i take cube of two as eight i leave first and the last digit the middle two digits i double it so double of four is eight two times two is four and then what i do i write this number eight as it is i add four plus eight so this gives me nothing but 12 so i will take only last digit one will become carry over so four plus two six carry over one seven it gives me seven here and one comes as it is hence the square here sorry cube here is one seven two eight now let me take another number so i take a number suppose i take a number 16 so if i have to find out 16 cube so i will write number as it is one six square of six is 36 cube of six is 216 now what do i do here there is there are three digits here there are two digits so the thing is very very simple what i need to do is first of all i will always take last digit if if these two digits if these two numbers at the last are two digit number or or a three digits number i will take only last digit here so what do i take six here and what about this 21 so 21 will go out here as carry over so first let me find out the double of these numbers and then let me show you how i do what what i'll do here is i will find out the double of these numbers so this is 72 and double of this number is 12 so what i do i take six here and then i take 21 as carry over here so when i add this what comes out so 1 plus 6 7 7 plus 2 9 and 3 plus 2 5 5 plus 7 12 so 12 now from here 12 carry over will go here so this becomes 30 so from here 3 carry over will go here so see what i do i take last digits from everywhere this is 6 this is 9 this is 0 and 1 plus 3 is how much 4 so answer comes out to be how much 4096 i will again repeat it what i did is i wrote number as it is 16 i took square of 6 36 i took cube of 6 which is 216 now from here i have taken last digit 6 here and 21 goes as carry over to the next term so i have 36 double of 36 72 and this 21 as carry over when i add all these things it comes out to be 129 so out of 129 i take last digit 9 and that 12 goes to goes as carry over to the other term so this gives me nothing but 12 plus 12 24 plus 6 30 so i take last digit 0 here and 3 goes as carry over so 1 plus 3 is equal to 4 so that gives me how much 4096 now let me go to numbers ending with 1 so numbers ending with 1 would be something like 21 cube let me take 21 cube now the method is almost same with with a little bit of difference so when i took 12 cube here what did i do i wrote 1 2 and then i took square of 2 and cube of 2 so i wrote from left to right here i will write from right from left right to left so i will write here i was writing 12 at the left end here i will write 21 at the right end and there i was taking last digit square of last digit and cube of last digit here i will take square of first digit and cube of first digit the thing is i will not take square of 1 if it was starting with 1 i was taking square and cube of the other number here it is ending with with 1 so i am taking square and cube of the number with which it is starting so i have to take basically whether it is starting with one or ending with one the one digit is one whether at the end or at the start so the other digit i'm taking square and cube of the other digit so i will write 21 at right and end here and i will take square of 2 as 4 and cube of 2 as 8 similarly here i will leave first and the last digit and i'll take a double of 2 and 4 so this gives me 4 and this gives me 8 and i will add this so this gives me 1 this gives me 6 this gives me 12 so 1 is carry over so i add here so this gives me 9 so this answer here is 9 to 6 1 so i am again repeating it the only difference from here is that here 12 was written as left end here 21 i'm writing at right end and then i'm taking apart from 1 the number is 2 so i'm taking square of 2 and cube of 2 rest everything remains same so let me take another number now let me take 51 cube so if i take 51 cube so i write 5 and 1 here i take square of 5 which is 25 and cube of 5 which is 125 then i double it so this gives me 10 then i double this this gives me 50 so i write last digit here 1 as it is 5 plus 10 is 15 so 1 becomes carry over here and this gives me 76 so 6 comes here and 7 becomes carry over here and this gives me 132 so 51 cube would be equal to 132651 132651 this is the right answer so i hope you understood these two methods in next video i'll be teaching you the next two methods which is the same numbers and the different numbers so till the time you take few numbers from yourself and try to practice these things so that you can become efficient in these techniques and i'll see you all in the next video so thank you so much for joining me and learning this particular technique from me and see you all in the next video thank you so much