Question

question 5
simplify.
$-3isqrt{-40}$
$\circ\\ 6\sqrt{10}$
$\circ\\ 6\sqrt{10}i$
$\circ\\ -6\sqrt{10}$
$\circ\\ 6i\sqrt{10}$

Explanation:

Step1: Simplify the square root of -40

Recall that \(\sqrt{-a} = i\sqrt{a}\) for \(a>0\). So, \(\sqrt{-40} = i\sqrt{40}\). Then, simplify \(\sqrt{40}\): \(\sqrt{40}=\sqrt{4\times10} = 2\sqrt{10}\). Thus, \(\sqrt{-40}=i\times2\sqrt{10}=2i\sqrt{10}\).

Step2: Multiply with -3i

Now, we have \(-3i\times\sqrt{-40}=-3i\times2i\sqrt{10}\). Multiply the coefficients and the imaginary units: \(-3\times2=-6\) and \(i\times i = i^{2}\). Recall that \(i^{2}=-1\). So, \(-6\times i^{2}\sqrt{10}=-6\times(-1)\sqrt{10}=6\sqrt{10}\).

Answer:

\(6\sqrt{10}\) (corresponding to the first option: \(6\sqrt{10}\))