How do you simplify #sqrt(-2x^5)#?

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Answer 1 · 2015-07-03T22:43:18

If #x <= 0# then #sqrt(-2x^5) = x^2sqrt(-2x)#

If #x > 0# then #-2x^5 < 0# so #sqrt(-2x^5) !in RR#

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

If #x <= 0# then #-2x >= 0# and #x^4 = (x^2)^2 >= 0#

So:

#sqrt(-2x^5)#

#= sqrt(-2x*x^4)#

#= sqrt(-2x)*sqrt(x^4)#

#= sqrt(-2x)*x^2#

#= x^2sqrt(-2x)#