cube-tricks,13thlesson-mathematics-tricks-and-fun

 Cube-Tricks,13thLesson-MathematicsTricks-and-Fun

  Today we are going to study the methods to find cube of numbers.I am Dr Prema B Sejekan. We shall study methods using yavadunam sutra to find the cube of numbers.

We should learn and keep ourselves ready with the square and cube of unit digits for a quick solving of the cubes of numbers..Here I have noted down the squares and cubes of commonly used digits.

  In finding cube of a number,first

 find the number of digits in the question and3/(3-1) times that will be the number of digits in the answer and

  when first digit is 1,2,3 it will be

   3-1,3-2 times digits , in the answer.

 Mark the expected digits in the answer as dots.

   This is Cubing by yavadunam tavadunokritya varge cha yojayet.

Here cube of 103 is the question.Here the base is 100.  3 is the excess and the main working digit is 3 here we multiply 3 with 3 which stands for the cube so 3 X 3 is 9 .now 100+9 equals 109 is the first part of the answer. Next we multiply this new 9 with first excess 3 which gives 27 Then 27 becomes middle part of the answer. and cube of first excess 3 is 27 which becomes the last part of the answer. The answer is 1092727.Here as I have told there are 3 digits in the question and since the first digit is one   digits in the answer  = are 7 digits.ie 3-2times

Same yavadunam sutra is used here also.996×996×996=

1000 base 1000-4 so -4×3= -12. 1000-12so first part is 988.Then -12×3 = -048, middle part. Then cube of -4 is -64so 936 Answer is 988047936.

 

As said earlier we count the number of digits 6 digits and bigger number answer will have thrice this ie ,18 digits. 

999992 = 1000000-8.The deficiency- 8 is the working digit..-8multiplied by ,3 which is -24 This subtracted from 1000000 gives

 =999976 this becomes first part .Then -8×-24=000192, this is the middle part of the answer .cube of -8 is -512., we borrow one from ,192 which becomes 191 . Now 1000000-512 =999488 Thus the answer is 999976000191999488.

We have to find cube of 9999. 10,000 and minus 1 is equal to 9999 so the working digit in this is minus one. so by. Yavadunam Sutra minus 1 into 3 because, We are finding the cube we get -3 that deducted from 10000 gives  9997. now the middle part we have to find out that is we have to multiply minus 3 with the original deficiency minus one that will give plus 3 so we will add it to 10,000 that will give 0003 in the middle part and then the last part to find out the cube of -1. cube of -1 is again -1.. so -1 deducted from 10000 we will have to borrow one from plus 3 that will become 2 and -1 deducted from this 10000 will give us 9999 so the answer is 999700029999 By practice we will know the cube of 9 as 729 . And quickly we can write the answer.

In the coming classes we will study- How to find the cube of a numbers having same digits.