How do you simplify sqrt(-2156)?

Apr 4, 2018

$46.43 i$

Explanation:

$\sqrt{- 2156} = \sqrt{- 1} \cdot \sqrt{2156}$

${i}^{2} = - 1 \text{ or } i = \sqrt{- 1}$

$i \cdot \sqrt{2156} \approx i \cdot 46.43 \approx 46.43 i$

Apr 4, 2018

$\sqrt{- 2156} = 14 \sqrt{11} i$

Explanation:

The prime factorisation of $2156$ is:

$2156 = {2}^{2} \cdot {7}^{2} \cdot 11$

Hence:

$\sqrt{2156} = \sqrt{{14}^{2} \cdot 11} = 14 \sqrt{11}$

and:

$\sqrt{- 2156} = \sqrt{2156} i = 14 \sqrt{11} i$