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Find the cube root of 203:
(1) 203 is not a perfect cube, so the answer is not rational. Therefore you will find an approximation or leave in radical/rational exponent form.
Note that `root(3)(203)` is algebraic since it is the solution to `x^3=203` .See link below.
(2) On a calculator or computer algebra system you could enter `root(3)(203)` (this is usually a key marked `root(y)(x)` or `root(x)(y)` ) getting:
(3) On a calculator you could use rational exponents, thus:
`203^(1/3)~~5.877130659` Note that `x^(1/3)=root(3)(x)` .
(4) You could use guess and check. You know that `5^3=125,6^3=216` so the cube root of 203 is between 5 and 6. Then `5.8^3=195.112` and `5.9^3=205.379` so the cube root lies between 5.8 and 5.9. You can continue this process to any desired accuracy.
** The answer you write down is only an approximation unless you use radical notation `root(3)(203)` or rational exponent notation `203^(1/3)` **
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