(a+b)^1/2 another question is Square root (-4)^2=? (a+b)^1/2 and Square root (-4)^2=?
I'm new to learning algebra. I know what (a+b)^2 is. But then I thought what happens with ^1/2 or ^1/4. Can someone explain me?
Also I have 2 questions in my book. Square root of 4^2= I calculated it by multiplying by ^1/2= 2/2=1, so I get 4^1 is 4. Then I got a question: Square root of (-4)^2. Doing the same steps here I ended up with -4. Is that correct?
I'm sorry if it is not wel explained. If something is unclear I'll try explaining diffrent.
 A: Well you might have looked into
$\left(a+b\right)^2\:=\:a^2+b^2+2ab$
This is actually derived using BIOMIAL THEOREM. Similarly 
$\left(a+b\right)^{\frac{1}{2}}\:\:or\:\left(a+b\right)^{\frac{1}{x}}$
for all real values of 'x' are derived using BINOMIAL THEOREM. If you are new to algebra BINOMIAL is a bit complex. 
Actually we say $\left(a+b\right)^{\frac{1}{2}}$ as the square root of (a+b) written as $\sqrt{\left(a+b\right)}$.
And in the problem the first case is 
$\left(4^2\right)^{\frac{1}{2}}=\left(16\right)^{\frac{1}{2}}$
Now $\left(16\right)^{\frac{1}{2}}$ is actually either +4 or -4 as both of them square yields 16.
That is 
$4^2=\left(-4\right)^2=16$
So for the second part 
$\left(\left(-4\right)^2\right)^{\frac{1}{2}}$
yields the same answer +4 or -4.
A: When you raise $x$ to the $\frac{1}{2}$ power, that means you are taking the square root of $x$.  So $x^{\frac{1}{2}} = \sqrt{x}$.  Similarly, $(a + b)^{\frac{1}{2}} = \sqrt{a + b}$.
Because of this, you can easily figure out what, for example, $4^{\frac{1}{2}}$ is.  Since this is just $\sqrt{4}$, and you know that $\sqrt{4} = 2$, then we have $4^{\frac{1}{2}} = 2$.
Can you figure out what $9^{\frac{1}{2}}$ is?  What about $16^{\frac{1}{2}}$?
Now, when you take the square root of anything, it is always a positive number.  So if you have $\sqrt{ (-4)^{2}}$, first you square the $-4$ on the inside.  This makes the problem become $\sqrt{16}$, and you know that $\sqrt{16} = 4$.  This is why $\sqrt{ (-4)^{2}} = 4$.  It's because you first square the inside, and the square root is always a positive number.
A: *

*There is no rule for simplifying $\sqrt{a+b}$

*$(-4)^2 = -4 \cdot -4 = 16$

*$4^2$ cannot be calculated by applying an exponent of $\frac{1}{2}$ because it changes the question "what is the square of 4?" 
