Question

question
write $sqrt{-63}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Factor out -1 from radicand

$\sqrt{-63} = \sqrt{-1 \times 63}$

Step2: Split into product of square roots

$\sqrt{-1 \times 63} = \sqrt{-1} \times \sqrt{63}$

Step3: Simplify $\sqrt{63}$ by factoring

$\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}$

Step4: Substitute $\sqrt{-1}=i$

$\sqrt{-1} \times 3\sqrt{7} = 3i\sqrt{7}$

Answer:

$3i\sqrt{7}$