Question

What are the steps for simplifying radicals?

Answer 1

See if you can factor out a perfect square

Explanation:

In general, when we simplify radicals, we want to factor out a perfect square. For instance:

Let's say we're simplifying the radical `sqrt84`:

Because of the radical law, we can rewrite a radical expression `sqrt(ab)` as `sqrta*sqrtb`.

In our example, we can rewrite `84` as `4*21`. We now have the radical

`sqrt(4*21)=sqrt4*sqrt21=2sqrt21`

Since `21` has no perfect square factors, we cannot factor it any further.

The same goes if we had `sqrt54`. We can rewrite `54` as `9*6`, which allows us to separate the radical as

`sqrt9*sqrt6=>3sqrt6`

Once again, `6` has no perfect square factors, so we are done.

Let's solidify this further with another example:

`sqrt162`

We can rewrite `162` as `81*2`, which allows us to separate the radical as

`sqrt81*sqrt2=>9sqrt2`

Hope this helps!