How do you simplify the square root of -96?

Answer 1

In simple terms, negative numbers don't have square roots. If you multiply a number by itself, you can never get a negative number for the answer. Square a negative or a positive, you get a positive; square zero, you get zero.

Now, if you get fancy, you could say that while a negative number has no real square roots, you can make one up by inventing the imaginary number i, which is the number that when squared, equals -1. Then you can say that sqrt (-96) = [ sqrt(-1) ] * [ (sqrt(96) ] = i*sqrt(96). From here, you can go ahead and simplify sqrt(96) ...

Look for a perfect square factor, and take it out of the root: 96 = 4x24 = 4x4x6 = 16x6; sqrt(96) = sqrt(16)*sqrt(6) = 4sqrt(6).

So sqrt(-96) = i*4sqrt(6), which is customarily written as 4isqrt6

(You would write a radical sign wherever it says "sqrt" above.)