How do you simplify #sqrt(-2156)#?

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Answer 1 · 2018-04-04T08:53:27

#46.43i#

#sqrt(-2156) = sqrt(-1) * sqrt(2156)#

#i^2 = -1 " or " i = sqrt(-1)#

#i * sqrt2156 ~~ i * 46.43 ~~ 46.43 i#

Answer 2 · 2018-04-04T10:37:58

#sqrt(-2156) = 14sqrt(11)i#

The prime factorisation of #2156# is:

#2156 = 2^2 * 7^2 * 11#

Hence:

#sqrt(2156) = sqrt(14^2 * 11) = 14sqrt(11)#

and:

#sqrt(-2156) = sqrt(2156) i = 14sqrt(11)i#