You can
put this solution on YOUR website!
You are correct in that the square root of the 9 will become a 3 at some point. This can be the first thing you do or it can come later. Since you did this first then that is how I will do it too:
The next thing I would do is multiply the remaining square roots together using the property of radicals,
:
Next we look for perfect square factors (other than 1) in
. There are no perfect square factors in 3. For the
and the
you are looking for exponents that are multiples of 2,
not perfect squares! For example,
,
and
are all perfect squares not because their exponents are perfect squares (which they are not) but because the exponents are all divisible by 2!
So
and
are not perfect squares because their exponents are not divisible by 2. But they both have factors that are perfect squares:
For reasons that will become clear shortly I like to use the Commutative Property to rearrange the order of the factors so that all the perfect square factors are n front:
Next we use the same property as before, only in the other direction, to split up this square root of a product into a product of square roots. We want all the perfect square factors in their own square roots. The factors that are not perfect squares all go into the same square root:
The square roots of the perfect squares will all simplify:
or
This is the simplified answer. (Note how the square root is at the end. This is the normal way to write terms like this and it is the reason I put all the perfect square factors in front earlier.)
You can
put this solution on YOUR website!
You can combine all this under one radical
Combine like terms
factor to reveal more perfect squares
extract the square roots of each perfect square
which is:
(