1.587401052 to 9 decimal places according to my calculator.
cuberoot(8) + cuberoot(8) + cuberoot(8) = 6
9000
sqrt(3/4), cuberoot(17)
It is a root of a number where that root cannot be made into a rational number. For example, the cuberoot(27/64) is 3/4 and so is not a radical but cuberoot(32/64) = cuberoot(1/2) = 3√(1/2) cannot be simplified or rationalised further.
The answer depends on the functions that you may use. A possible solution: cuberoot(8) + cuberoot(8) + cuberoot(8) = 2 + 2 + 2 = 6
Unfortunately, this browser does not support many mathematical symbols but the answer is 4*cuberoot(4).
If the length of a side is x inches then the volume is s3 cubic inches. So s = cuberoot(vol) ie s = cuberoot(514.125) = 8.011 inches (to 4 sf).
There is no easy way. For example the cube root of 30 is irrational. Now, because 27 < 30 < 64 then, taking cube roots, 3 < cuberoot(30) < 4. But that is as far as it goes! If the number ends with 000 then the cuberoot is a multiple of 10. So that cuberoot(27000) = 10*cuberoot(27) = 10*3 = 30. But there are many numbers ending with 000 between 27000 and 64000 for which this will not work.
7
~2.519
They are cuberoot(3) = 1.442 metres (approx)
2 * cube_root(5/4) = 2*cube_root(5) / cuberoot(4) = approx 2.1544347