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

Algebra ->  Polynomials-and-rational-expressions -> 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       Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
If you have something like x%5E2=4, how do you solve this? Well you simply take the square root of both sides like this

sqrt%28x%5E2%29=sqrt%284%29


x=0%2B-sqrt%284%29


Notice how sqrt%28x%5E2%29 simplifies to x. What's happening is the square root is undoing the square exponent.



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


So the same thing is happening with sqrt%28+%28+a%2B4+%29%5E2%29. If you can't see it, then let x=a%2B4 to get

sqrt%28x%5E2%29


so this simplifies to x where x is positive


Now plug a%2B4 into x to get a%2B4



So this means that sqrt%28+%28+a%2B4+%29%5E2%29 simplifies to a%2B4 . In other words, sqrt%28+%28+a%2B4+%29%5E2%29=a%2B4 where a%2B4%3E0