How do you simplify: the square root of -32?

1 Answer
George C.
Jul 25, 2015

The square roots of -32 are +-4sqrt(2) i

Explanation:

The identity sqrt(ab) = sqrt(a)sqrt(b) is only valid for a, b >= 0.

About the best we can do more generally is sqrt(ab) = +-sqrt(a)sqrt(b)

To see why, consider the invalid reasoning:

-1 = sqrt(-1)sqrt(-1) = sqrt(-1*-1) = sqrt(1) = 1

With this in mind:

sqrt(-32) = sqrt(4^2*2*-1) = +-sqrt(4^2)sqrt(2)sqrt(-1) = +-4sqrt(2)i

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