How do you simplify sqrt((-3)(-12))√(−3)(−12)?

1 Answer
George C.
Feb 19, 2017

sqrt((-3)(-12)) = 6√(−3)(−12)=6

Explanation:

sqrt((-3)(-12)) = sqrt(36) = sqrt(6^2) = 6√(−3)(−12)=√36=√62=6

What is interesting here is what you must not do:

sqrt((-3)(-12)) != sqrt(-3)sqrt(-12) = isqrt(3)*isqrt(12) = i^2sqrt(36) = -6√(−3)(−12)≠√−3√−12=i√3⋅i√12=i2√36=−6

Note that for Real values of a, ba,b, the identity:

sqrt(ab) = sqrt(a)sqrt(b)√ab=√a√b

only holds when at least one of a, ba,b is non-negative.

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