Question

question
write $sqrt{-245}$ in simplest radical form.
answer attempt 1 out of 4

Explanation:

Step1: Factor out -1 from radicand

$\sqrt{-245} = \sqrt{-1 \times 245}$

Step2: Split into product of square roots

$\sqrt{-1 \times 245} = \sqrt{-1} \times \sqrt{245}$

Step3: Simplify $\sqrt{245}$ by factoring

$\sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \times \sqrt{5} = 7\sqrt{5}$

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

$\sqrt{-1} \times 7\sqrt{5} = 7i\sqrt{5}$

Answer:

$7i\sqrt{5}$