What are the steps for simplifying radicals?

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Answer 1 · 2018-07-06T00:52:46

See if you can factor out a perfect square

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!