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√-98 = _____?

7√2i
4√7i
49i
None of these

Explanation

Let's simplify $\sqrt{- 98}$ step by step.

Express under the square root as a product of a positive number and $- 1$ :
$\sqrt{- 98} = \sqrt{98 \cdot (- 1)} = \sqrt{98} \cdot \sqrt{- 1}$
Simplify $\sqrt{98}$ :
Factor 98:
$98 = 49 \times 2 = 7^{2} \times 2$
So,
$\sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \cdot \sqrt{2} = 7 \sqrt{2}$
Recall that $\sqrt{- 1} = i$ :
So,
$\sqrt{- 98} = 7 \sqrt{2} \cdot i = 7 \sqrt{2} i$

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