Question

Compare the following:

`root(3)(48) and sqrt(36)`

Answer 1

`root(3)(48) = 48^(1/3)  "has power" (1)/(3)`

`sqrt(36)` = 6

Now, L.C.M. of 3 and 1 = 3

`root(3)(48) = 48^(1/3)`

`sqrt(36) = 6 = 6^(3/3) = (6^3)^(1/3) = 216^(1/3)`

Since 48 < 216, we have `48^(1/3) < 216^(1/3)`
Hence, `root(3)(48) < sqrt(36)`.