SOLUTION: Find the following. Assume that variables can represent any real numbers. sqrt ( a+4 )^2 The a+4 should be in parenthesis with an exponent of 2 in a radical sign. I hope I

Question 133112: Find the following. Assume that variables can represent any real numbers.
sqrt ( a+4 )^2
The a+4 should be in parenthesis with an exponent of 2 in a radical sign. I hope I explained that correctly.
Found 2 solutions by nycsharkman, jim_thompson5910:
Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
Are you trying to simplify this radical?
I will assume that you are trying to simplify it.
sqrt{(a + 4)^2}
The inside of the radical becomes a^2 + 8a + 16 after applying the FOIL method.
We now house every term SEPARATELY in a radical and simplify.
sqrt{a^2} = a
sqrt{8a} = 2(sqrt{2a})
sqrt{16} = 4
We now have this:
a times 2 times 4 times sqrt{2a} =
8a(sqrt{2a})
Did you follow?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you have something like , how do you solve this? Well you simply take the square root of both sides like this

Notice how simplifies to . What's happening is the square root is undoing the square exponent.

---------------------

So the same thing is happening with . If you can't see it, then let to get

so this simplifies to where x is positive

Now plug into x to get

So this means that simplifies to . In other words, where
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