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.

$2sqrt (85)i$