The discussion centers on the mathematical property that leads to the conclusion that \( a \) is equal to \( -a \) under specific conditions involving square roots. The user explores the equation \( \sqrt{a} = \sqrt{b-c} \) and identifies the critical step where the property \( \sqrt{ab} = \sqrt{a}\sqrt{b} \) is applied incorrectly due to the non-negativity restriction on \( a \) and \( b \). This results in the expression \( a = \pm a \), necessitating a decision on the correct sign based on context.
PREREQUISITESStudents, educators, and anyone interested in advanced algebra, particularly those dealing with complex numbers and square root properties.
The step above is where the problem is. You're using the property that ##\sqrt{ab} = \sqrt{a}\sqrt{b}##noahsdev said:I've been messing around with numbers (as you do) and I'm wondering why this occurs..
lets let a = b-c.
√a
= √(b-c)
=√(-(c-b))
=i√(c-b)
noahsdev said:=i√(-(b-c))
=i2√(b-c)
=-√(b-c)
=-√a
For example if you let a = 1, b = 2, and c = 1.
That makes sense. Thanks.Mark44 said:The step above is where the problem is. You're using the property that ##\sqrt{ab} = \sqrt{a}\sqrt{b}##
There are restrictions on this and some of the other square root properties - both a and b have to be nonnegative.