Why Does the Order of Square/Square Root Matter?
Date: 8/28/96 at 15:40:32 From: Ken Mead Subject: Why Does the Order of Square/Square Root Matter? Why does the square root of x^2 equal absolute value of x, but the square of the square root of x equals just plain old x? Sweating in Precalc, Ken
Date: 8/28/96 at 22:33:1 From: Doctor Robert Subject: Re: Why Does the Order of Square/Square Root Matter? It is mostly a matter of semantics, but when you see a square root sign, which I will abbreviate sqrt( ), the answer is, by agreement, a positive number. sqrt(9) = 3 because sqrt(3*3) = 3. If you are asked sqrt(-3*-3) you might expect to write -3, but by agreement, answers are only positive, therefore you must write abs(-3)=3. When you put x^2 under the radical, you don't know whether x will be positive or negative; therefore you must write sqrt(x^2) = abs(x). I hope that this helps. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994-2013 The Math Forum