SOLUTION: How do you simplify 42+28 radical 3 all over -12

Question 422775: How do you simplify 42+28 radical 3 all over -12
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
A radical is the symbol that looks a little like a division symbol. Radicals are used to indicate all different kinds of roots. All of the following expressions have a radical:

But none of these are represent the same number because they are different kinds of roots. (The number that looks like an exponent in front of the radical is called the index and the index tells you what kind of root the radical represents. (The first radical above has no visible index. Radicals like these have an implied index of 2.))

So when you post questions about radicals, it will often be impossible to solve your problem without know what kind of radical is involved. Here is some English to describe the expressions above:
is the "square (2nd) root of 13"
is the "cube (3rd) root of 13"
is the "fourth (4th) root of 13"
is the "fifth (5th) root of 13"
is the "tenth (10th) root of 13"

The expression inside a radical is called the radicand. Since the radicand of your radical is 3 and since 3 is a prime number, this is one of the rare instances where we do not have to know what type of radical is involved in order to simplify the expression. (There is no way to simplify any kind of root of a prime number.)

In the solution below, I am going to use "n" to represent the type of root. Just replace "n" with whatever your problem has for the type of root.

As I mentioned earlier the root of a prime number, no matter which kind of root, will not simplify. And the terms in the numerator are not like terms so we cannot add them together. So all we can do is reduce the fraction.

To reduce a fraction we need to find factors we can cancel. So we start with factoring:

We can cancel the factors of 2:

leaving:

This is a simplified expression. However, some people prefer not to have a negative denominator. For them we could multiply the numerator and denominator by -1 and get:

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