What is the square root of -340?

1 Answer
Sep 14, 2015

Answer:

#2sqrt(85)i#

Explanation:

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#