How do you simplify sqrt(-3)sqrt(-12)√−3√−12?
1 Answer
Oct 30, 2017
Explanation:
What is interesting about this example is that it is a counterexample to the often quoted "identity":
sqrt(a)sqrt(b) = sqrt(ab)√a√b=√ab
In fact this identity only holds if at least one of
By convention, the principal square root of a negative number
sqrt(n) = isqrt(-n)√n=i√−n
So:
sqrt(-3)sqrt(-12) = i sqrt(3) * i sqrt(12) = i^2sqrt(3)sqrt(12) = -1 * sqrt(3 * 12) = -sqrt(36) = -6√−3√−12=i√3⋅i√12=i2√3√12=−1⋅√3⋅12=−√36=−6
