Question 78765
{{{sqrt(.8x^4)}}}
The first thing I see from this is that you can pull the x^4 term out from under
the radical and get:
{{{x^2sqrt(0.8)}}}
Do you understand why that can be done? Think about it this way:
When you take the square root of a number, you are really raising
that number to the 1/2 power, like this:
{{{sqrt(x^4)=(x^4)^(1/2)}}}
There is a property about exponents that when a number with an exponent is raised 
to another exponent, it can be simplified by keeping the base number and multiplying the exponents. In other words:
{{{(x^4)^(1/2)=x^(4*(1/2))=x^2}}}
So that is how I was justified in getting the x^4 out from under the radical as an x^2.
You can now simplify {{{x^2sqrt(0.8)}}} even more if you recognize that:
{{{0.8=0.2*0.2*2*2*5}}}
Using the same logic as above, I can pull out a 0.2 and a 2 from under the radical. This leaves you with:
{{{0.2*2x^2sqrt(5)}}}
{{{0.4x^2sqrt(5)}}}

It's open to debate if that final answer is simpler than {{{x^2sqrt(0.8)}}},
but at least it is good practice in dealing with radicals!

Good Luck,
tutor_paul@yahoo.com