Question

How do you simplify 2 square root -49?

Answer 1

You cannot simplify this question as there is no real number which represents `sqrt(-49)`.

Answer 2

`2 sqrt {- 49} = 14 i`

Explanation:

If we use real numbers, this problem has no solution since there is no real number that is squared `- 49` and therefore, there is no square root of `- 49` in `RR`.

But if we expand the set of numbers we use and use complex numbers `CC`, we have that the imaginary number `i` is:

`i = sqrt {- 1}`.

Taking this definition of number `i` into account we can see that:

`2 sqrt {- 49} = 2 sqrt {49 cdot (- 1)} = 2 sqrt 49 cdot sqrt {- 1} = 2 cdot 7 cdot i = 14 i`