SOLUTION: When you take the square root of both sides of an equation, what sign(s) must be given to the result on the right side if the variable is on the left side?

Question 4744: When you take the square root of both sides of an equation, what
sign(s) must be given to the result on the right side if the variable is
on the left side?
Found 2 solutions by longjonsilver, rapaljer:
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
WHENEVER you do a square root, there are ALWAYS 2 solutions (unless the question stipulates that one can be ignored).

means what number multiplied by itself is 25?. Answer is either +5 or -5...BOTH answers give +25.

I cannot stipulate this enough...when you take square roots, there are 2, YES 2, answers. OK? :-)

jon

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
There are actually two different definitions of square root. The first is called the "Principle Value Definition of Square Root" which is defined to be a positive number. Usually when you ask for the square root of a number, especially if a calculator is used, you give the positive number. Often we assume in particular problems, especially radical equations, that this principle value definition is used.

According to the Principle Value Definition, , , etc.

However, there is also a "general definition" of square root, for example, the which refers to ALL numbers whose square is 9. This means either +3 or -3. Usually the only time this definition is applied, is when you ask to find ALL square roots of 9. This would be a hint that you want plus 3 or minus 3.

When you take the square root of both sides of an equation, you MUST put a plus or minus in order to obtain all the solutions. If you do NOT put the plus or minus, you will be throwing away half of the answers every time!! Longjon is correct when he said that when you take both sides of an equation, ALWAYS include the plus or minus.

R^2 at SCC
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