Question

What values of a, b, and c yield a true statement in the equation below?

a= ?
b=?
c=?

Answer 1

(a, b, c) = (8, 3, 2)

Explanation:

Remove cubes from under the radical. Combine terms.

`\sqrt[3]{16} +2\sqrt[3]{54} =\sqrt[3]{2^3\cdot 2}+2\sqrt[3]{3^3\cdot 2}\\\\=2\sqrt[3]{2}+2\cdot 3\sqrt[3]{2}=(2+6)\sqrt[3]{2}\\\\=8\sqrt[3]{2}\equiv a\sqrt[b]{c}\ \longrightarrow\ \boxed{(a,b,c)=(8,3,2)}`