What is the square root of negative 8?

1 Answer
Mar 18, 2018

Answer:

See a solution process below:

Explanation:

#sqrt(8)# can be rewritten as:

#sqrt(4 * 2 * -1)#

We can use this rule for radicals to simplify the expression:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#sqrt(color(red)(4) * color(blue)(2) * color(green)(-1)) =>#

#sqrt(color(red)(4)) * sqrt(color(blue)(2)) * sqrt(color(green)(-1)) =>#

#2sqrt(color(blue)(2)) * sqrt(color(green)(-1))#

The symbol #i# which is an imaginary number is another way to write: #sqrt(-1)# so we can rewrite the expression as:

#2sqrt(color(blue)(2)) * i =>#

#2isqrt(color(blue)(2))#

If necessary we can approximate #sqrt(2)# as #1.414# and get:

#2 * 1.414i =>#

#2.828i#