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)#