How do you simplify: the square root of -175 ?

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Answer 1 · 2015-07-22T15:24:49

#5i*sqrt(7)#

Factor the number to primes:

#sqrt(-125)=sqrt(-1*5*5*7)#

Pull out the duplicate 5 and #i#:
#sqrt(-1*5*5*7)=5i*sqrt(7)#

Answer 2 · 2015-07-22T15:26:33

#sqrt(-175) = 5sqrt(7)i#

#sqrt(-175) = sqrt(175)*sqrt(-1)#

#color(white)("XXXX")##= sqrt(175)i#

#color(white)("XXXX")##= sqrt(5^2*7)i#

#color(white)("XXXX")##= 5sqrt(7)i#