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Cube & Cube-Root of any number by easy & fast way

We are applying Vedic formula for finding Cube & Cube-Root of any number by observation only. First we study the method to find cube of any number & then study to find Cube-Root of perfect cube.

Cube of number-

Vedic sutra Anurupya is applicable to find the cube of any number. As usual we will explain the steps while solving the sum. Read it 2-3 time carefully to understand the method. once you understand the method you can solve the sums in few seconds.

Ex. i) 42³   

 Step 1: Very first step is divide the number in to two parts by slash, 4/2

Here a = 4 & b = 2

Step 2: Now find the value of first Row.  If we move from right to left-

1) Left hand digit of first row is 4³ = 64.

Now we move from left to right with ratio b/a i.e 2/4 = ½

2) 2^nd digit in first row is = (½) x first digit

= (½) X 64 = 32

3) 3^rd digit in first row is = (½ ) x Second digit

=  (½) x 32 = 16

4) 4^th digit in first row is = (½) x Third digit

= (½) x 16 = 08 = 2³

Now our first row is, 64   32     16    8

Step 3: Second row is obtained by doubling the middle term of first row & add them.

Step 4: Now to obtained final answer we put 3 Zero behind the first term from LHS, 2 zero behind second term, one zero behind third term & no zero behind last term then add them. Adding zero rule is same for 2 & 3 digit number.

Answer, 42³ = 74088

Ex. ii)  23³

 Step 1:  Consider a =2 & b =3

Step 2:

1) Left most digit in first row is a³ = 2³ = 8

2) Second digit = (b/a) x first digit

= (3/2) x 8 = 12

3) Third digit = (3/2) X 12 =18

4) Fourth digit = (3/2) x 18 = 27 = b³

Now our first row is, 8     12      18     27

Step 3: Second row is obtained by doubling the middle term of first row & add them. 

Step 4: Add appropriate zero on the final row & add them.

                 8000 + 3600 + 540 + 27 = 12167

Answer, 23³ = 12167

Similarly,

Ex.iii) 103³      = 10/3     (For 3 – digit number, LHS of slash contain 2-digit)

   Here a=10 & b = 3

1) First digit of first row = 10³ =1000  & ratio is b/a = 3/10

2) Second digit = (b/a) x first digit

= (3/10) x 1000 = 300

3) Third digit = (3/10) X 300 =90

4) Fourth digit = (3/10) x 90 = 9 = b³

Now our first row is, 1000     300      90    9

Step 3: Second row is obtained by doubling the middle term of first row & add them.

Now to obtained final answer add the total row by adding zero on terms,

1000000 + 90000 + 2700 + 9 =1092727

Answer, 103³ = 1092727

Cube root of perfect cube-

We will consider perfect cube only to find the cube root as practically it asked more. Initially we memorized the cube of number 1 to 10.

Now by observing the last digit of above table we make one more table

From above table we can conclude that cube of number 0,1,4,5,6 & 9 end with same number, where as cube of 2 end with 8 & cube of 3 end with 7 & vice versa.

Ex. i) Find the cube root of 85184

Step 1: Put a slash before last 3 digit

           85/184

Step 2: Here last digit is 4, & we know from table 2, last digit of cube is 4, So last digit of cube root will be also 4.

So, we get our last digit _4.

Step 3: To find first digit of the answer, we observe LHS of the given cube. It is 85 here. 85 lies between –

Step 4: Out of these two number 4 & 5 we take smaller number as first digit of our answer.  (Always take smaller number from two)

      So, our first digit is 4.

    Answer, cube root of 85184 = 44.

Ex. ii) Find the cube root of 1728

 Step 1:   1/728

 Step 2: Last digit of answer = _2 (From table 2)      

 Step 3: LHS part of slash is 1, which is cube root of 1

 Step 4: So, our first digit = 1.

 Answer, cube root of 1728 = 12.

Ex. iii) Find the cube root of 681472.

Step 1:   681/472

Step 2: Last digit of Answer = _8 (From table 2)      

Step 3: 681 lies between 512 & 729, which are the cube of 8 &9

Step 4: From 8 & 9 smaller number is 8, So our first digit is 8.

Answer, cube root of 681472 = 88

Ex. iv) Ex. iii) Find the cube root of 1225043

Step 1:   1225/043

Step 2: Last digit of Answer = _7 (From table 2)      

Step 3: 1225 lies between 1000 & 1331, which are the cube of 10 & 11.

Step 4: From 10 & 11 smaller number is 10, So our first digit is 10.

Answer, cube root of 1225043 = 107.

Find this Link to Study more:

1.Find the square & Square-root of any number by observation only

2.Base Method of Multiplication: Multiply a number near the base in 3-4 seconds

3. Bow method of multiplication for any multiplication