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Practice mental Cubic root calculation


Practice Mental Square or Cubic root Calculation: vs. 1.0
Type:
Square
Cubic
Select either Square or Cubic roots practice
 
Press the Button to get the next test number
Options:
1 digit  
2 digits
3 digits
Select cubic numbers for 1-3 digits
    Answer:
Type in the correct answer
 
    Score:

 
 
Press the Button to clear the result
    
Press the Button to print the result
    
 
  • Result
  • Help

Practice Mental calculation of cubic root in your head

Click the get next test number button to randomly generate a 1, 2 or 3 digit cubic number so you can practice calculated the cubic root of that number.

Email me if you encounter any problems at hve@hvks.com

There is an excellent website for mentally calculating 1-2 digit square root at http://mindmagician.org/sqrt.aspx and for 1-2 digit cubic root at http://mindmagician.org/cubert.aspx
Another webiste for mentally calculating cubic root for 3 digits number can be found on http://thinkinghard.com/blog/CubeRoots.html
All theses web sites describe the method in details.

 


Mental calculation of the cubic root of a 1, 2 or 3-digit number

Cubic root of a 3-digit number
This is very simple to do and all you need is to memorize or calculate on the fly what single digit number raised to the power of 3 give the cubic root of that number. The table 1, below can be used and is easy to memorize. All it takes is some practice.
Table 1 Single digit cubic root:

N

N3

N3

0

03

0

1

13

1

2

23

8

3

33

27

4

43

64

5

53

125

6

63

216

7

73

343

8

83

512

9

93

729

Cubic root of a 6-digit number
Here is another cool party trick that is easy to perform. Ask one in the audience to choose a random 2-digit whole number x and raise it to the power of x3. Ask for the resulting number after the operation and you can right away tell which 2-digit number was raised to the power of 3. A 2-digit number ab can also be written as 10a+b where a and b are single digit number. Raise it to the power of 3 you get:
1000a3+100a23b+10a3b2+b3
The lowest possible 2-digit number is 103=1,000 and the highest possible value is 993=970,299. By looking at the number on the left of thousand separator you can establish what single digit number raised to the power of 3 is less or equal that number to determine the first digit. You can also see that b3 will represent the last digit since the other component is multiplied by 10, 100 and 1000 and does not contribute to the last digit. The reason why this is working is by looking at the table below that any single digit raised to the power of 3 all end in a unique digit from 0 to 9 where the unique single digit is underscored.
Table 2 double digit cubic root


N

N3

N3

Mapping

0

03

0

Same

1

13

1

Same

2

23

8

10-8

3

33

27

10-7

4

43

64

Same

5

53

125

Same

6

63

216

Same

7

73

343

10-3

8

83

512

10-2

9

93

729

Same

We also notice by looking at the thousands that it consists of the 1000a3 plus something more (100a23b+10a3b2+b3). This information indicates that if we find the nearest number less or equal than the 1000a3 then we can establish the digit a.
An example is better to show how it works.
573=185,193. Now taking the thousand only (185) and find closet smaller number from the table which is 125 and 53. We now know the cubic root of the number start with 5. Next look at the last digit of the last 3 digits (193). Which is 3 and match it up with the last digit in the 3rd Column that end with the number 3. The number is 343 and represent 73 and now you know that the last digit must be 7 and therefore the correct answer is 57. With some practice is goes lightning fast. A way to remember the mapping for the last digit is to say that 1, 4, 5, 6 & 9 end in the same digit and the other ends in 10-digit.

343=39,304. The thousand part is 39 and the closest n3 less is 33=27. The first digit is then 3. Looking at the last digit 4 you know by the table that 43 ends in 4 and therefore the last digit is 4 and the result is 34 which is the answer.

I mention in the start that the number needs to be a 2-digit whole number. This is not entirely accurate. The method works just as well for any 2-digit decimal number e.g. 7.93=493.039
Notice that there is no thousand parts and therefore the number must be less than 10. Separating the number before and after the fraction sign (instead of before and after the thousand separator) you get 493 which closest n3 number less than 493 is 73=343. The first digit is then 7. Looking at the last digit 9 and the table above 93 ends in 9 and therefore the last digit is 9 and the result is then 7.9.
You can even do 2-digit fraction number e.g. 0.133=0.002197. Again, separating the number into two parts 002 and 197 you quickly see that the first digit is 1 and the second digit is 3 (last digit is 7 and the corresponding number from the table which last digit is 7 is 3) and since the result is less than 1 all digits must be fraction digit and the result is 0.13

Cubic root of a 9-digit number
Cubic root of a 9 digits number is generated by raising a 3-digit number to the power of 3.? It gets a little bit complicated to find the 3-digit number giving the 9-digits number and require more practice to handle it perfectly. Instead of describing the method below I will instead refer the reader to this web site at http://thinkinghard.com/blog/CubeRoots.html where the Author Phillip Dorrell provide an elegant and comprehensive description of how to handle mental calculation of the cubic root of a 9-digit number.

Have fun

Corrections:
21-Jun-2017 Vs 1.0 Initial release of practice mental cubic root calculator
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