Question

Square root of -72 in the form of a+bi

Answer 1

`0+6√(2)i`

or just
`6√(2)i`

Explanation:

`√(-72)` does not have a real part, it is a pure imaginary number.

Let's simplify.

First step:

`√(-1)=i` is the imaginary unit.

So we have that we can write
`√(-72)=i √(72)`.

Second step:

Let's simplify the factor
`√(72)` by looking for perfect squares of
`72`.

`72=2(36)=2(6^2)`

So
`36` is a perfect square because it can be written as
`6^2`.

`√(-72)`

`i √(72)`

`i √(2 \cdot 6^2)`

`i √(2) √(6^2)`

`i √(2) 6`

`6 √(2)i`

We could write this as
`0+6√(2)i`.