What is the square root of negative 8?

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Answer 1 · 2018-03-18T21:50:20

See a solution process below:

$sqrt(8)$ 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:

$2 * 1.414i =>$

$2.828i$