How do you simplify the square root of -6 times square root of -50?

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Answer 1 · 2015-09-16T06:03:59

$sqrt(-6) * sqrt(-50) = -10sqrt(3)$

If $x < 0$ then $sqrt(x) = i sqrt(-x)$ is the principal square root of $x$ , where $i$ is the imaginary unit.

$-i sqrt(-x)$ is also a square root of $x$ .

If $a, b >= 0$ then $sqrt(a)sqrt(b) = sqrt(ab)$

The condition $a, b >= 0$ is important. For example:

$1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1)*sqrt(-1) = -1$

So:

$sqrt(-6) * sqrt(-50) = i sqrt(6) * i sqrt(50) = i^2 * sqrt(6)sqrt(50)$

$= -1 * sqrt(300) = -sqrt(10^2 * 3) = -sqrt(10^2)sqrt(3) = -10sqrt(3)$