How to do this without relying on the fact that the number is a perfect cube:
Learn a handful of logs base 10 (not much more work than the cube digit laws). Maybe you know 2,3,5 and e.
19,683 is equal to 20,000
log 20,000 is log 2 + log 10 + log 10 + log 10 + log 10
That's 0.30 + 1 + 1 + 1 + 1 which is 4.30
Divide by 3 (equivalent to taking cube root). That's 1.43
Recall that log e is 0.43. So 1.43 is log (e * 10). Hopefully you remember e = 2.71, so the number you're looking for is 27.1. If you remember that you rounded up to start, you can round back down and guess that it's more like 27.0.
You can simplify this a little further by dividing out thousands and multiplying by 10s at the end, so you only need to find the cube root of 20 using the same process.
Learn a handful of logs base 10 (not much more work than the cube digit laws). Maybe you know 2,3,5 and e.
19,683 is equal to 20,000
log 20,000 is log 2 + log 10 + log 10 + log 10 + log 10
That's 0.30 + 1 + 1 + 1 + 1 which is 4.30
Divide by 3 (equivalent to taking cube root). That's 1.43
Recall that log e is 0.43. So 1.43 is log (e * 10). Hopefully you remember e = 2.71, so the number you're looking for is 27.1. If you remember that you rounded up to start, you can round back down and guess that it's more like 27.0.
You can simplify this a little further by dividing out thousands and multiplying by 10s at the end, so you only need to find the cube root of 20 using the same process.