Question

How do you simplify `root(3)(162)`?

Answer 1

`root(3)162=3root(3)6`

Explanation:

To simplify `root(3)162`, we should first factorize `162` into prime factors.

The factor of two can be worked out as

`162=2xx3xx3xx3xx3`

As we are taking out cube root of `162`, we should make group of three same numbers. In the given case, we can have it only one group of prime factor `3` and hence for cube root we can takeout only one `3`.

`root(3)162=root(3)(2xxul(3xx3xx3)xx3)`

or `root(3)162=3root(3)(2xx3)`

Hence `root(3)162=3root(3)6`