SOLUTION: What are the steps to symplfying large root problems?

Question 406070: What are the steps to symplfying large root problems?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Simplifying Square-Root Terms
1.
To simplify a square root, you "take out" anything that is a "perfect square"; that is, you take out front anything that has two copies of the same factor:

When you solve the equation , you are trying to find all possible values that might have been squared to get 4. But when you are just simplifying the expression, the ONLY answer is ""; this result is called the "" .
Other roots, such as , can be defined using graduate-school topics like "complex analysis" and "branch functions".
2.
Sometimes the argument of a radical is a , but it may "contain" a square amongst its factors.
To simplify, you need to factor the argument and "take out" anything that is a square; you find anything you've got a pair of inside the radical, and you

.
To do this, you use the fact that you can switch between the multiplication of roots and the root of a multiplication. In other words, radicals can be manipulated similarly to powers:

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