Roots and Radicals
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
When simplifying square roots, we give the positive and negative answer if solving an equation that did not originally have a square root. Otherwise, we give only the principal root. Square roots of negative numbers have non-real answers, which is why square roots of variables sometimes include the condition that the variable is greater than zero. Knowledge of math radicals is important when solving quadratic equation problems.
Hopefully by now you have seen the square root symbol that I have behind me and what I want to talk about right now is just some common mistakes that people use when they, sorry people do when they use the square root. Okay so what I want to talk about is the difference between the square root of 25 and the difference of x squared is equal to 25.
Okay, the square root is what we call the principle root okay and what that means is the main thing that comes out of it and typically that is going to be positive when you're dealing with this square root so the square root of 25 is just 5 okay a lot of students like to put plus or minus in front of it, it's not the case it's just the positive 5. Okay, the difference is dealing with x squared is equal to 25. In order to solve this we want to take it square root so what we do is we put a square root in, okay and then in this case whenever you take the square root you need to end up with plus or minus. Okay so the difference is, is that whenever there is a square root in the problem, it's the principle root, if it's, you're dealing with a square root is just going to be positive.
When you are solving something and you put in the square root you then need to include plus or minus okay so when you're including a square root as a tool so you put it in as a tool to solve something you need to think plus or minus when the square root is already there it's just positive.