Radical Math Equation

Question

How do you know what power to raise both sides of an equation to if the indices of the radicals are different? For example, given the equation , what index would you use? Why? Explain your reasoning. Make sure to address this specific example, then provide an additional, unique example that also shows how your reasoning is correct.

Answer 1

By the LCM.

√(x + 1)⁶ = ^{6 = 3}√(x - 1)⁶

(x + 1)³ = (x - 1)²

Etc.