Math CentralQuandaries & Queries


Question from Ashley, a student:


How do you simplify this equation assuming that variables can represent any real number?



The square root of a product is the product of the square roots of the factors. So you need to know how to find √125 and √(x2).

There are various correct forms for √125. A useful one, often expected in assignment problems, is to factor out as big a perfect square ("take as much outside") as you can; thus √12 would be 2√3.

For √(x2) the problem is different; you might think it would just be x, but not necessarily. Hint: let x be -2, what do you get?
If you don't see the answer yet, try plotting √(x2) for x = -3,-2,-1, 0,1,2,3 and see if you recognize the graph.

Good Hunting!


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