Simplify 1 over [(cube root 2) + 1]
To simplify the expression 1 / (cube root 2 + 1), we can rationalize the denominator.
Rationalizing the denominator means getting rid of any radicals in the denominator.
To do this, we can multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of the denominator is obtained by changing the sign of the radical term (cube root 2) to its opposite sign.
So, let's rationalize the denominator:
1 / (cube root 2 + 1) * (cube root 2 - 1) / (cube root 2 - 1)
Multiplying the numerators and the denominators, we get:
(cube root 2 - 1) / ((cube root 2)^2 - 1^2)
Simplifying the denominator:
(cube root 2 - 1) / (2 - 1)
Finally, simplifying the expression:
(cube root 2 - 1) / 1
The simplified expression is (cube root 2 - 1).