cube tricks of same digit number 14 lesson on mathematics Tricks and Fun

Cube tricks of same digit number 14 lesson on mathematics Tricks and Fun

Hello friends today we are going to study the methods to find cube of same digit numbers.I am Dr Prema B Sejekan. We can use a special method to find the cube of these numbers.
 

Cube of unit digits

 1.    1              6.              216

 2     8              7.              343

 3    27             8.              512

 4    64.            9.              729

 5    125.         10.            1000

 First count the number of digits in the

  number to be cubed. N

 Twice or 2-1 times of that , will be the

 number of digits in the first part of the answer.

 Find the Cube of the unit digit in the question

 This digit or digital sum of that is taken      

  as the working digit.First add this from

 both sides progress Arithmetically till N 

 number of digits on either side.

  This number will be used to find the cube 

 If N number of digits in the question we will

  have thrice or 3-1 or 3-2 times that in the 

  answer. Bring down outermost one digit on 

 either side.Add this to the second and write

   down. Repeat this on both sides till N number

 To get middle digits - exclude outer one digit 

 and add Ndigits Together.Repeat same after 

 excluding 2digits.Repeat same on the other side .

 

 

 

 

This example of a cube of 111  ,   same digit number will explain.cube of 1 is 1 we write this as 0 a gap and 1. Add 1 this is the working digit 0+1 =1, 1+1=2 sowe write this as 012.we go to the other side 1+1=2,2+1=3 we stop adding here since it is 3 digit number.so the first part of the answer is 012321.

Now we have to add these as shown in the diagram bring down 0, then 0+1 =1, 1+2=3 .stop here since 3 digit number.we go to the other side bring down 1, then 1+2= 3, 3+3= 6. Stop here.Now exclude outer one digit each then add 3 digits together from both sides to get middle digits.Add 1+2+3=6 and from other side 2+3+2=7 thus the answer is 1367631.following this method however long the number to be cubed we can do easily.

This example cube of 111111 will show how we used the same method.

Finding cube of 222222 .  cube of 2 is 8 we write 08 as 0 on left and 8 on right .Then go on add 8 for total 6 digits and we get 098765234568. To get cube, you have to add from both sides first 6 digits with each other and write new 6 digits on either side.Then we have to get middle digits For this exclude one digit each from both sides and add 6 digits together and write.Next outer 2 digits excluded from both sides and add 6 digits. Next exclude 3 digits and add 6 digits.Thus you get 10973903978085048

Cube of 3333 we know this means 3333×3333×3= 3333× 9999. It is easyto multiply this as we have learnt6  using special code. 3×9= 27then using special code - one more one less ,33326667.now we cand. Do the calculation to find the cube. First 4 digits on either side add each with the other ie bring down 3 then 3+3 write down 6, then 6+3 write down 9, then 9+2 write down 11 then go and repeat same on the other side? After this exclude outer one digit on either side and add 4 digits together on both sides. Exclude two digits and add 4 digits In this only one time we can add 4 digits.Thus answer is 37025927037

Cube of 6666 we can do this in the routine way.cube of 6 is  216.write 21 on left and 6 on right with a gap in between .Then Add 21+6 we get 27 now working digit is 27add 27 to 21 gives 48 write 8 and add 4 to 21 now this 48 added to27 gives 75 5 wriitten and 7 carried over then 75 added to 27gives 102 same way add 27 with 6 33again add 33 to 27 =60 like that adding carry overs you get 266613336.,this is the pattern you get however big the number.now add astold earlier to get the cube Answer is 296207416296

Cube of 444 cube of 4 is 64.write 6. On left and 4 on the right with a gap. Add digital sum (6+4=10). 10 and progress Arithmetically till 3 digits on either side. Adding carry overs you get 788544.Then adding this for cubing as discussed gives 87528384.

Cube of 555 as cube of 5 is 125 write 12 as one digit on left and 5 on right with a gap in between then digital sum add 12+ 5 is 17 this is added  and Arithmetically progressed for 3 digits here on both sides thus we get 1540125.Now add 1+5= 6,6+4=10 like that as said earlier Thus answer is 170953875

This is Cubing of 777777 . cube of 7 is,343 write 34 gap and 3 digital sum got by adding 34+3 gives 37 this is the working digit .add to 34+37 gives 71 ,then 71+37= 108 like that for 6 digits on both sides answer is 4234559432103. Now calculate the cube as shown earlier. Answer is 470506133060396433

Cube of 8888. cube of 8 is 512 now 51 written as single digit. And gap. 2 now 51+2 gives 53 use 53 as working digit and progress Arithmetically from both sides for 4 digits.631972352. Now add these numbers as said earlier and we get the answer 702121283072

In the coming classes we will recapitulate all the multiplication in Vedic maths.