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Square roots of positive numbers

  • Thread starter bluskies
  • Start date
  • #1
11
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Homework Statement



If a and b are positive real numbers, and [tex]\lambda^{2} = ab[/tex], then [tex]\lambda = \pm \sqrt{ab}[/tex].

Homework Equations



None.

The Attempt at a Solution



This is more of a conceptual question that has always escaped me. I do not understand how the square root of two positive numbers could possibly be negative. Since a and b are positive, how can there be any negatives in the square root of their product? Any guidance on this subject would be very much appreciated.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
(-1)2 =1

so squaring -√(ab) will give (ab) regardless of a + or - before the square root.
 
  • #3
1,033
1
I think you might be looking too hard into this. There are no negatives in the square root. the negative is outside it. say both a and b are 5. then lambda² = 25. lambda therefore is equal to positive root(25) or negative root(25). Or in other terms, lambda² = 5² or (-5)²
 
  • #4
954
117
A numerical example can illustrate this. Let a = 1 and b = 4 for instance. Then we have [tex]\lambda^{2} = 4[/tex]. We realise however, that because negatives cancel upon multiplication, in fact [tex](-2)^2 = 2^(2) = 4[/tex], and so both -2 and 2 are possible solutions.
 
  • #5
11
0
Thank y'all for your help, that makes sense now. :)
 

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