The cube root just means what number you would multiply by itself three times in order the get that number. 27 is just 3*3*3.
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Enter the number, press ^ and enter 1/3 i.e. the cube root of 27 would be 27^(1/3)
Most square roots, cube roots, etc. - including this one - are irrational numbers. That means you can't write them exactly as a fraction. Of course, you can calculate the cubic root with a calculator or with Excel, then find a fraction that is fairly close to it.
an alg expression involving square roots, cube roots, etc
It lies between the cube roots of 311 and 313.
The cube root of the expression 403 is 40 itself. This follows from the definition of cubes and cube roots.