Question

question 2
completely simplify the following expression: \\(\sqrt{-72}\\)
\\(i\sqrt{72}\\)
\\(6i\sqrt{2}\\)
\\(2\sqrt{-36}\\)
\\(6\sqrt{-2}\\)

Explanation:

Step1: Separate negative from radical

$\sqrt{-72} = \sqrt{-1 \times 72}$

Step2: Split into two radicals

$\sqrt{-1 \times 72} = \sqrt{-1} \times \sqrt{72}$

Step3: Substitute $\sqrt{-1}=i$

$\sqrt{-1} \times \sqrt{72} = i\sqrt{72}$

Step4: Simplify $\sqrt{72}$

$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$

Step5: Combine terms

$i \times 6\sqrt{2} = 6i\sqrt{2}$

Answer:

B. $6i\sqrt{2}$