Question

How to simplify `sqrt(-81)`?

Answer 1

`9i`

Explanation:

You cannot simplify this into a real number, but if you use the imaginary number (`sqrt(-1)`) which is represented using the letter `i` you can simplify it to `sqrt81 * sqrt(-1)` which is the same as `9i`

Answer 2

This is complex number questions that deals with the imaginary i.

Explanation:

first, lets rewrite it,
`sqrt(-1xx81)`
which then turns into
`sqrt(-1)xxsqrt(81)`
the `sqrt(-1)` is actually the complex number i.
Therefore u can transform it to i which leaves u with
`isqrt(81)`
from there, u simplify the 81 as per normal
so ur answer should be `9i`

Answer 3

See a solution process below:

Explanation:

First, rewrite the expression as:

`sqrt(81 * -1)`

Next, use this rule for radicals to simplify the radical:

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

`sqrt(color(red)(81) * color(blue)(-1)) =>`

`sqrt(color(red)(81)) * sqrt(color(blue)(-1)) =>`

`9sqrt(color(blue)(-1))`

The square root of `-1` is also called the imaginary number `i`.

Therefore:

`9sqrt(color(blue)(-1)) =>`

`9i`