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September 25th, 2010, 08:55 AM   #1
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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.
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September 25th, 2010, 10:37 AM   #2
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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.
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September 26th, 2010, 07:44 PM   #3
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Re: When should Square Root be taken Plus or minus & when no

Remember that exists if and only if . What happens when you have is this definition:

. Since module is distance, it means the distance of that point is . Thus, it could be positive square root or negative, afterall, the distance is the same.
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September 26th, 2010, 08:56 PM   #4
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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.
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September 27th, 2010, 01:09 AM   #5
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Re: When should Square Root be taken Plus or minus & when no

y = x^2 is a parabola.
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