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

Question

asked Aug 22, 2021 74.2k views

1 Answer

Shibankar · Answer 1 · 2021-08-26T09:30:39+0000

Answer:

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=2(36)=2(6^2)

So
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 .