TesseracT22
New Member
What is the logical fallacy in :
-1 = sqrt(-1)*sqrt(-1) = sqrt(-1*-1) = sqrt(1) = 1
-1 = sqrt(-1)*sqrt(-1) = sqrt(-1*-1) = sqrt(1) = 1
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- Thread starter TesseracT22
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sqrt(a)*sqrt(b) only equals sqrt(ab) for the principal square roots of a and b ie the positive square roots.
For positive numbers, without this restriction, we could have
1 = sqrt(1)sqrt(1) = sqrt(1) = -1
For the square root of negative numbers, there is no principal square root, so
sqrt(a) *sqrt(b) does not necessarily equal sqrt(ab).
In your example, we see that the negative square root of 1 is in fact -1, which would make the equality hold.
For positive numbers, without this restriction, we could have
1 = sqrt(1)sqrt(1) = sqrt(1) = -1
For the square root of negative numbers, there is no principal square root, so
sqrt(a) *sqrt(b) does not necessarily equal sqrt(ab).
In your example, we see that the negative square root of 1 is in fact -1, which would make the equality hold.