My Math Forum When should Square Root be taken Plus or minus & when not ?

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 September 25th, 2010, 08:55 AM #1 Newbie   Joined: Sep 2010 Posts: 2 Thanks: 0 When should Square Root be taken Plus or minus & when not ? Respected Teachers, Members, friends & all, Hello. I'm new to the forum. I want to ask is that I'm really very very confused with the square root. I was taught that square root of only number is positive, but when we consider a quadratic equation if, for example, x^2 = 36 then the value of x = 6 or x = -6. But when I started studying the chapter RATIO, PROPORTION & VARIATION.......in that we have to find the mean proportional of: 1) 8, 18 2) 8, 32 then we take the mean proportional as x therefore x^2 = 8 X 18 = 144 therefore answer is given as x = 12 or we take x^2 = 8 X 32 = 256 therefore answer is given as x = 16 in fact wherever in this chapter square root is taken, the answer is considered only positive value. Now I'm very much confused what to consider. When to take plus or minus & when not to consider negative term. Please help me on this. I have an exam to take next week & I have to really clear this concept. Thanks in advance. God bless Last edited by skipjack; June 28th, 2015 at 12:15 AM.
 September 25th, 2010, 10:37 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: When should Square Root be taken Plus or minus & when no Typically in geometry, we preclude negative side lengths and angle measures (less typically...) from consideration. Since proportions are ratios involving side lengths, we don't use negative values for these either. God bless you, as well.
 September 26th, 2010, 07:44 PM #3 Newbie   Joined: Aug 2010 Posts: 22 Thanks: 0 Re: When should Square Root be taken Plus or minus & when no Remember that $\sqrt{x}$ exists if and only if $x \geq 0$. What happens when you have $x^2= a \rightarrow x = + \sqrt{a} \; \mbox{or} \; x = - \sqrt{a}$ is this definition: $\sqrt{x^2}= |x|$. Since module is distance, it means the distance of that point is $\sqrt{a}$. Thus, it could be positive square root or negative, afterall, the distance is the same.
 September 26th, 2010, 08:56 PM #4 Newbie   Joined: Sep 2010 Posts: 2 Thanks: 0 Re: When should Square Root be taken Plus or minus & when no Thank you very much for replying to my question. it was really very helpful. thanks once again.
 September 27th, 2010, 01:09 AM #5 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Re: When should Square Root be taken Plus or minus & when no y = x^2 is a parabola.

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