Question

question
fully simplify.
$(sqrt{3})(5sqrt{-10})$
answer attempt 1 out of 2

Explanation:

Step1: Recall imaginary unit

Recall that $\sqrt{-a} = i\sqrt{a}$ for $a>0$, so $\sqrt{-10}=i\sqrt{10}$.

Step2: Multiply the coefficients and radicals

Multiply the terms: $(\sqrt{3})(5\sqrt{-10}) = 5\times\sqrt{3}\times i\sqrt{10}$.

Step3: Multiply the radicals

Using $\sqrt{m}\times\sqrt{n}=\sqrt{mn}$, we get $\sqrt{3}\times\sqrt{10}=\sqrt{30}$.

Step4: Combine the results

So, $5\times\sqrt{3}\times i\sqrt{10}=5i\sqrt{30}$.

Answer:

$5i\sqrt{30}$