Question

evaluate the following square root expression. \\(\sqrt{-18}\\)

Explanation:

Step1: Separate negative from radicand

$\sqrt{-18} = \sqrt{-1 \times 18}$

Step2: Split into product of square roots

$\sqrt{-1 \times 18} = \sqrt{-1} \times \sqrt{18}$

Step3: Simplify $\sqrt{-1}$ and $\sqrt{18}$

$\sqrt{-1} = i$, $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

Step4: Multiply simplified terms

$i \times 3\sqrt{2} = 3i\sqrt{2}$

Answer:

$3i\sqrt{2}$