What are the steps for simplifying radicals?

1 Answer
Jul 6, 2018

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!