Question

Rewrite the irrational cube root 189−−−√3
as the product of an integer and another irrational cube root. Show your work.

Note: You will find the option to add a cubic root symbol in the Algebra (×
) keyboard.

Answer 1

Start with ∛189. Factor 189 = 27·7 (since 27 = 3^3). Then use ∛(ab) = ∛a·∛b:

∛189 = ∛(27·7) = ∛27 · ∛7 = 3 · ∛7.

Thus ∛189 = 3∛7. (∛7 is irrational because 7 is not a perfect cube.)