Question

How does finding the square root of a number compare to finding the cube root of a number. Use the number 64 in your explanation.

(I've been thinking about this question for an hour now and brain is hurting)

Answer 1

It becomes a question of perfect squares and perfect cubes.
Obviously you can take a square root of a perfect square, and the cube
root of a perfect cube, the fourth root of a perfect quartic, etc

Some perfect squares are also perfect cubes, such as your 64, or 729
As a matter of fact if you cube a perfect square, or if you square a
perfect cube, you will be abel to take the square root and the cube root of such a number.
e.g. the perfect square 49 cubed = 117649
and √117649 = 343
and cuberoot(117649) = 49
both results are exact , (rational numbers)
the same is true for decimals

e.g. 1.44 is a perfect square, since √1.44 = 1.2
let's cube 1.44 to get 2.985984
clearly, taking the cube root will get us back to the exact value of 1.44
and √2.985984 = exactly 1.728

hope this sheds some light on your problem