What is the square root of -340?

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Answer 1 · 2015-09-14T06:38:38

#2sqrt(85)i#

A negative square root has an imaginary number.

#sqrt(-1)=i#

#sqrt(-340)=#

#sqrt((-1)(340))=#

#sqrt(340)i#

Write the prime factors for #340#.

#sqrt(340)=(sqrt(2xx2xx5xx17))#

Square like terms.

#sqrt(2^2xx5xx17)=#

#2sqrt (5xx17)#

#5# and #17# are prime factors, so multiply them and keep them under the square root symbol. Add the symbol for an imaginary number.

#2sqrt (85)i#