 friends welcome to Centrum Academy. So in the last video as you know that we have discussed about cubes of two different kinds of numbers which are numbers starting with one or ending with one. So we have discussed these two cubes and in this video I am going to do two different type of cubes which I explained in the last video. So one would be of same numbers and one would be different numbers. For an example same numbers can be 33, 77 likewise different numbers can be 37, 54 and likewise. So let me start with these two techniques and this will complete this segment of videos of finding out cubes of two digits numbers. So I am going to teach you technique of finding out cubes of numbers which have same digits. So suppose I take number 11. So let me take 11 cube. Now what are the two digits? It's a two digit number but the digits are same one. So take one and take cube of one three four times. So one cube is one, one cube is one, one cube is one, one cube is one. So what is our method? We leave first and the last digit. So I leave first and the last digit here and then we take a double or twice of the middle two numbers. So double of one is two, one into two is two and then you add this. So how much it gives you? It gives you one, three, three, one. It is as simple as this. Now let me take another number. So suppose I take 33 and I want to find out cube of 33. So if I take 33 this gives me 27, cube 27. I take cube of three four times. So this is 27. I leave first and the last numbers. I take two times the middle two numbers. So 27 into two is 54. Then what do I do? I take last digit seven. What about this two? This two becomes carryover here. So 27 plus 54 is 81 plus 283. So three comes here. Eight is my carryover. Again 54 plus 27 is 81 plus eight is 89. So eight is my carryover here and 27 plus eight is 35. So 33 cube gives me how much? 33 cube gives me 35,937. So it is as simple as this. You take cube of the digit four times. You leave first and the last numbers. You take middle two numbers. Take double of those middle two numbers and then proceed with the normal method that we have been doing till now. So I take last digit seven. Two is my carryover here. So 54 plus 27 plus two is 83. I take three. Eight becomes carryover here and 81 plus 80 is 89. So nine comes here and eight becomes carryover for the other number. So 27 plus eight is 35. So that gives me 35,937. Now I'm moving to techniques of finding out cubes of number which have different digits. So for that matter, let me take a number 23 and I want to find out 23 cube. Now in this particular method, please make sure you listen to me very carefully and you look at the procedure very carefully. So what is the first digit here? Two. So I write cube of two here which is eight. Then what is the last digit here? Second digit here? Three. I write 27. Three cube is 27 and I leave the middle two portions. In all the cubes I have found out, I have four different numbers. I have been writing four different numbers. First, second, third and fourth. So here the cubes that I have written for the two numbers are the first and the last numbers. So two cube is eight. It's the first number. Three cube is 27. It's the last number. And in between I will write two more numbers. I'm telling you how to write this. The first number here would be take square of the first number. So two square is four. Multiply it with the second number here. So how much it gives? Four into three is 12. So I write 12 here. The second number here takes square of the second number. So that gives me nine. Multiply it with first number. So nine into two is how much? 18. So now as I know I leave first and the last digit, last numbers and I take double of two middle numbers. So I write here 27. So seven I take two as carry over. 36 plus 18 is 54 plus two is 56. So this gives me carry over of five. I write carry over of five here. 24 plus 12 is 36 plus five is 41. So carry over of four and eight plus four gives me 12. So 23 cube comes out to be 12167. That's the answer. Now let me take another number. So suppose I take 54 and I find out cube of this. So what do I do? I take first number. I write cube of first number 125. Then I take a last number four and cube of four is 64. I have to write two numbers in between. So that the first number would be square of first number. So five square is 25 multiplied by four. That gives me 100. I took five square into four. That gives me 100. And the second number here would be square of second number. So four square multiplied by first number. So that gives me 80. So this number is 80. Now I write double of 80. That gives me 160 and two times 100 is 200. Now the procedure is simple. This gives me four. Six goes as carry over here. So 160 plus 80 is 240. And 240 plus 6 is 246. So 24 is my carry over here. 100 plus 200 is 300. Plus 24 is 324. So 32 is the carry over and four comes here. So 32 when I add to 125, it gives me 157. So 54 cube is equal to 157464. That's the answer. Let me take one more number and find out cube so that you can master this technique because different digits, I mean finding cubes of numbers which have different digits is a little bit complex. So I'm taking one more number to show you how I'm finding it out so that you can master this technique. So let me take a number. Suppose I take a number 47. And if I have to find out 47 cube, so I write 64 here, which is four cube, and I write 343 here. And I have to write two digits in between. So that would be four square into seven, which is 16 into seven is 112. And then I have seven square into four, which is 49 into four is 196. So I take double of these numbers in between. So this gives me 392. And this gives me 224. So what do I do now? I write three here, 34 is my carry over here. So four plus six, 10 plus two 12. So one, and then 18 plus 321 plus 122. And three plus one, four plus two is six. So 62 becomes carry over here. And I will take last digit. So three from here and two from here. So this gives me 224 plus four is eight. And then six, one, seven plus two is nine. And two plus one is three. So I take last digit here, which is eight. And then I take this 39 as carry over here. So this gives me three. And six plus three is nine. And nine plus one gives me 10. So 47 cube comes out to be 103823. That's the answer. So I hope you understood these methods. And with this, the techniques of cubes of two digits numbers are over. So I discussed four techniques here for four different kinds of numbers. I hope you understood all these techniques pretty well. So I would recommend that you take few numbers from your side and start solving these cubes with the techniques that I have discussed with you. And with that, you will find out that your ability to find out cubes of two digits number is improving day by day. So thank you so much for joining me in learning these techniques through these videos. And wish you all the best from Centrum Academy. Thank you so much.