Tuesday, February 15, 2011

TO FIND CUBE ROOT(short cut method)

 This technique helps you find out the cube root of a  4 or 5 or 6 digits number mentally.

Before going further on the method to find the cube root , please make a note of the following points –

1) Cube of a 2-digit number will have at max 6 digits (99^3 = 970,299). That implies if you are given with a 6 digit number, its cube root will have 2 digits.

2) This trick works only for perfect cubes, it will not work for any arbitrary 6-digit

3) It works only for integers

Now let us start with the trick to cube root of a 5 or 6 digit number in vedic mathematic way.
Say you have to find the cube root of 54872. It is known that it’s a perfect cube.

Now divide this number into two parts. The right hand side should always have 3 digits. Remaining digits will
come in left hand side. Do it as shown below.
54            |             872

You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (54) and digit at units place using right hand side of the number (872)

Step 1.
Memorize these tables (very soon you will know why) –


Table 1: Cube of 1 to 10
NumberCube
11
28
327
464
5125
6216
7343
8512
9729
101000

Table 2: Unit’s digit of Cube Roots
Cube Ends in Cube Root Ends in
11
28
37
44
55
66
73
82
99
00



Step 2.
For left hand side we need to use table 1. We have to see between which 2 numbers in the 2nd column do 54 lies. In this case it lies between 27 and 64. So we will take the cube root of the smaller number i.e. 27 which is 3.

So 3 is the tens digit of the answer.


Step 3.
For right hand side we need to use table 2. Since our original number (the perfect cube) ends in 2 (see 54872), its cube root will ends in 8.
Thus the units digit will be 8.
Combining the results we get the answer as 38.
Thus (54872)^1/3  =  38

Try for perfect cubes like 185193, 42875, 1728.


11 comments:

  1. If the number is not perfect cube, then what is the shortcut method for that....?

    ReplyDelete
  2. estimation method is the correct method. it is not a short cut method but some thing like a elimination of perfect cubes from the selected numbers.

    ex : Example 8: Find the cube root of 17576 through estimation.
    Solution: The given number is 17576.
    Step 1 Form groups of three starting from the rightmost digit of 17576.
    17 576. In this case one group i.e., 576 has three digits whereas 17 has only
    two digits.
    Step 2 Take 576.
    The digit 6 is at its one’s place.
    We take the one’s place of the required cube root as 6.
    Step 3 Take the other group, i.e., 17.
    Cube of 2 is 8 and cube of 3 is 27. 17 lies between 8 and 27.
    The smaller number among 2 and 3 is 2.
    The one’s place of 2 is 2 itself. Take 2 as ten’s place of the cube root of
    17576.
    Thus, 3 17576 = 26 (Check it!)

    ReplyDelete
    Replies
    1. i want a method for the number which is not perfect cube....

      Delete
  3. can give short cut explation for 1906624,and above 100 nubers give shortcuts

    ReplyDelete
    Replies
    1. Number:1906624
      Divide It into Two Parts:
      First Part:1906 Answer 12
      Second part:624 Answer 4
      Total Value Is :124(Check It)

      Delete
  4. Easy method to mentally find the cubroot of any 5 or 6 digit number

    Step 1:Find the cuberoot of the last digit.
    Step 2:Strike out the 3 digits from right.
    Step 3:For the first 2digits find the nearest cube to the number & put the number.
    Points to be remebered while using this method.
    (1)If the last digit is 8 then cuberoot will be 2.
    (2)If the last digit is 2 then cuberoot will be 8.
    (3)If the last digit is 7 then cuberoot will be 3.
    (4)If the last digit is 3 then cuberoot will be 7.
    (5)If the last digit is any other digit other than 2,8,3,7 then put the same number.



    List of cubes to be memorized
    13=1 43=64 73=343
    23=8 53=125 83=512
    33=27 63=216 93=729

    ReplyDelete
  5. tell me the cuberoot of a number

    3370

    ReplyDelete
  6. how to find the cube of a number not the cube root..like we have to find the cube of 25 so what will be the shortcut

    ReplyDelete
  7. pls give example for 6 digit.. 300763

    ReplyDelete
  8. tell me cube root of 4590 and 8000

    ReplyDelete