# Square roots of positive numbers

## Homework Statement

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

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.

Related Precalculus Mathematics Homework Help News on Phys.org
rock.freak667
Homework Helper
(-1)2 =1

so squaring -√(ab) will give (ab) regardless of a + or - before the square root.

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

A numerical example can illustrate this. Let a = 1 and b = 4 for instance. Then we have $$\lambda^{2} = 4$$. We realise however, that because negatives cancel upon multiplication, in fact $$(-2)^2 = 2^(2) = 4$$, and so both -2 and 2 are possible solutions.

Thank y'all for your help, that makes sense now. :)