Question

1. $sqrt{-6}$
2. $sqrt{-21}$

Explanation:

Step1: Rewrite negative radicand

$\sqrt{-6} = \sqrt{6 \times (-1)}$

Step2: Apply imaginary unit definition

$\sqrt{6 \times (-1)} = \sqrt{6} \times \sqrt{-1} = \sqrt{6}i$

Step3: Rewrite negative radicand

$\sqrt{-21} = \sqrt{21 \times (-1)}$

Step4: Apply imaginary unit definition

$\sqrt{21 \times (-1)} = \sqrt{21} \times \sqrt{-1} = \sqrt{21}i$

Answer:

1. $\sqrt{6}i$
2. $\sqrt{21}i$