Question

Rationalize the denominator of (3 * cube root of 12 - 8) / (cube root of 9 - cube root of 6).

Please show steps and the full process to rationalize.

Answer 1

(3∛12 - 8)/(∛9-∛6)

since a^3-b^3 = (a-b)(a^2+ab+b^2), multiply top and bottom by

(∛9^2 + ∛(9*6) + ∛6^2)

then you have

(∛36 - 6∛2 - 6∛3)/3