# How do you simplify 2 square root -49?

Jan 12, 2017

You cannot simplify this question as there is no real number which represents $\sqrt{- 49}$.

Jan 13, 2017

$2 \sqrt{- 49} = 14 i$

#### 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 $\mathbb{R}$.

But if we expand the set of numbers we use and use complex numbers $\mathbb{C}$, we have that the imaginary number $i$ is:

$i = \sqrt{- 1}$.

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

$2 \sqrt{- 49} = 2 \sqrt{49 \cdot \left(- 1\right)} = 2 \sqrt{49} \cdot \sqrt{- 1} = 2 \cdot 7 \cdot i = 14 i$