root 14 is a mistake, as it should just be 14. The square root of 196 is 14, not root 14. What is square root is is the opposite of squaring a number. For example, if 3 squared (3*3 or 3^2) = 9 and the square root of 9 = 3. For number 2, the third step would be the answer. Also, for the third question, do you understand what i is?
I don't really understand what it is but I believe I'm supposed to put it there when the number in the root is negative.
How do I know I'm not supposed to simplify the 5 in question 2? Is it because it doesn't work out to a complete number when you square it?
I apologize, again... We just started using the quadratic formula, and substitution today, and I have a test on it tomorrow afternoon.... thats why I'm in quite a hurry to verify my answers.
First of all, the square root symbol has to go over the ENTIRE $\displaystyle \displaystyle \begin{align*}
\sqrt{b^2 - 4ac} \end{align*}$, not just $\displaystyle \displaystyle \begin{align*} \sqrt{b^2} - 4ac \end{align*}$. However, due to how you have continued to simplify, I think that you already knew this and just had trouble actually typing this out.
In the first, $\displaystyle \displaystyle \begin{align*} \sqrt{100 + 96} = \sqrt{194} = 14 \end{align*}$, not $\displaystyle \displaystyle \begin{align*} \sqrt{14} \end{align*}$.
You should take note that we use the Quadratic Formula to get EXACT answers. This means in the second you really should keep it in terms of $\displaystyle \displaystyle \begin{align*} \sqrt{5} \end{align*}$ unless you're told to try to get a decimal approximation. Otherwise the second is correct.
In the third, you would either get to $\displaystyle \displaystyle \begin{align*} \sqrt{-16} \end{align*}$ and say there are no real solutions (as you can not take the square root of a negative number to get a real number), or if you are allowed to have complex solutions, write $\displaystyle \displaystyle \begin{align*} \sqrt{-16} = 4i \end{align*}$ and go from there.
In the last, surely you can see that $\displaystyle \displaystyle \begin{align*} 144 - 144 = 0 \end{align*}$, so that means you will be adding and subtracting 0, giving the SAME number. So you should only be getting ONE solution.
Do you even fully understand radicals? If not, you won't understand what i is until you grasp the basics.
http://teachers2.wcs.edu/high/fhs/ja...ls%201and2.pdf
Read this, it will teach you every property about radicals quickly. That is really the best thing I can show you, as you won't understand your mistakes until you understand the topic fully.