Finding the roots of $x^{2/3} + x ^{1 / 3} − 2$

Question

If the radical expression given to us is $$x^{2/3} + x ^{1 / 3} − 2$$ now the question is to find its roots.

I want to know: Can we multiply the whole equation in this way $$x^2 + x - 8$$ I.e. each term by ^3 or I have to take its whole cube (which can be really lengthy).

Please do share if there is any other method I could use as well.

Answer 1

Hint:

I presume the equation is $$x^{2/3}+x^{1/3}-2=0$$

How have you reached to $x^2+x-8=0?$

Better use the following substitution:

$$x^{1/3}=y\implies x=y^3$$

$$x^{2/3}=(x^{1/3})^2=?$$ to form a quadratic equation $y$