Take Cube Roots of 6-Digit Numbers Mentally

Step 9 Beyond 6-Digits

Once you have mastered the basic technique, you may wish to expand your mental extractions beyond 6-digits. This can be done, but at the cost that you will have to learn additional cubes. For example, from our previous list, suppose you learned that 11³ = 1331. You can apply the same technique as before, splitting on the comma between the hundreds and thousands places.

Example: 1,157,625
Doing the same technique as before, we split the number into 2 parts: 1,157 and 625. 625 ends in a 5, as does 5³, so the right hand side of our cube root is 5. 1,157 falls between 1000 (10³) and 1331 (11³), taking the lower of these, the left hand side of the cube root is 10. So, our cube root is 105.

As you can see at this point, for every additional cube above 10 that you learn, you can derive 10 more cube roots.

I hope you have enjoyed learning this fun little trick, so for all of you math geeks out there, have fun amusing and amazing your friends.

--Purduecer

Comments

[lucianoabcd]

What a weird kind of post !!! Gives me a few ideas... Is any generalized demonstration out there? I mean, symbolically or a by-heart calculation on all possible cubes between say 0 and 999,999 ?

[lancefisher]

Nice! Now if there were a trick to tell if the number is a cube or not...

[djmachet]

Brilliant! would like to try more of these techniques if you know them