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.


12 Comments:

At September 22, 2012 at 2:20 AM , Blogger anand said...

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

 
At October 25, 2012 at 5:57 AM , Blogger kspmaths said...

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!)

 
At February 24, 2013 at 9:28 PM , Blogger shyam dhane said...

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

 
At March 14, 2013 at 12:25 PM , Blogger sk.akramul islam said...

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

 
At April 23, 2013 at 4:51 AM , Blogger dharma reddy bojjireddy said...

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

 
At June 20, 2013 at 11:27 AM , Blogger Ashu said...

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

 
At June 20, 2013 at 6:02 PM , Blogger Naveen Kumar said...

tell me the cuberoot of a number

3370

 
At June 25, 2013 at 11:32 PM , Blogger abhishek mehra said...

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

 
At June 29, 2013 at 4:31 AM , Blogger jeeva said...

pls give example for 6 digit.. 300763

 
At August 14, 2013 at 8:04 AM , Blogger ajith basha said...

tell me cube root of 4590 and 8000

 
At August 14, 2013 at 8:08 AM , Blogger ajith basha said...

how to find cube of a number

 
At October 9, 2014 at 9:31 AM , Blogger Prathyusha said...

Please find out the cube root of 17373979

 

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