Radical Expressions

Question

How do you know what power to raise both sides of an equation to if the indexes of the radicals are different? For example, in , what index would you use?

Answer 1

You would do so by looking for the least common multiple. An easier way to think of it is as follows:

√(x+1) = ³√(x−1) is the same as (x+1)^1/2 = (x-1)^1/3

Therefore, you have to raise both sides by the least common multiple of 2 and 3.

The LCM of 2 and 3 is 6 (because 2*3=6). So you raise each side by a power of 6.

((x+1)^1/2)⁶ = ((x-1)^1/3)⁶

(x+1)³ = (x-1)²