It's called thinking outside the box, look it up!
(seriously tho, I've juste recently learnt a way to mentally find the square or cubic root of a number, as long as said root is between 10 and 100, in a matter of seconds. I don't want to be a huge ass nerd on a funny post so I'll only tell if someone asks).
Ok. For square roots :
1. You pick the all the digits, except the last two (for instance, with 729, it's 7.)
2. You determine which numbers are closest to it in the list of the first 10 perfect squares (for instance, 7 is between 4 (2²) and 9 (3²)). Keep the smallest root (2) and remember which number it was closest to : the bigger, or the smaller. Here, 7 is closest to 9, so remember "big".
3. Now we're working on the last digit. Here, it's 9. In the table of the 10 first perfect squares, there are 2 numbers ending in 9 : 3² and 7². We remembered "big", so we pick the biggest (7).
4. Voilà! Our number is 27. It sounds a bit complicated (I also lack the vocabulary I needed, which doesn't help) but try it and I promise you'll find it pretty easy.
For cubic roots :
1. Same
2. Same but don't bother with the big or small part
3. Same but there's only one number ending with the same digit!!
ex : 389 017. 389 is closest to 343, which is 7^3. We keep 7. 9^3 ends in 9. So : 79!
Granted, it takes a bit of practice to remember the 10 first cubes (if that's how you say it) but it's a fun skill to have, you can act like a super genius who counts super fast while you're in fact just using a neat little hack :D
(seriously tho, I've juste recently learnt a way to mentally find the square or cubic root of a number, as long as said root is between 10 and 100, in a matter of seconds. I don't want to be a huge ass nerd on a funny post so I'll only tell if someone asks).
1. You pick the all the digits, except the last two (for instance, with 729, it's 7.)
2. You determine which numbers are closest to it in the list of the first 10 perfect squares (for instance, 7 is between 4 (2²) and 9 (3²)). Keep the smallest root (2) and remember which number it was closest to : the bigger, or the smaller. Here, 7 is closest to 9, so remember "big".
3. Now we're working on the last digit. Here, it's 9. In the table of the 10 first perfect squares, there are 2 numbers ending in 9 : 3² and 7². We remembered "big", so we pick the biggest (7).
4. Voilà! Our number is 27. It sounds a bit complicated (I also lack the vocabulary I needed, which doesn't help) but try it and I promise you'll find it pretty easy.
For cubic roots :
1. Same
2. Same but don't bother with the big or small part
3. Same but there's only one number ending with the same digit!!
ex : 389 017. 389 is closest to 343, which is 7^3. We keep 7. 9^3 ends in 9. So : 79!