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cube & cube -root of any number by easiest way

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

= (½) X 64 = 32

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

=  (½) x 32 = 16

4) 4th 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.

Cube of number 1-10

 

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

cube root of number last digit by vedic method

 

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 

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