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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