To estimate the key root of 29 I would look at the perfect cubes blank and blank and then choose blink as a good estimate

I would look at the perfect cubes 25 and 27 and then choose 26 as a good estimate.

AAAaannndd the bot gets it wrong yet again!

No idea what a "key root" is, but
2^3 = 8
3^3 = 27
so 3 would be a good estimate for ∛29