question\nfully simplify.\n(2\\sqrt{-2})(5\\sqrt{3})

Explanation:

Step1: Multiply the coefficients

Multiply 2 and 5. $2\times5 = 10$

Step2: Multiply the square - roots

We know that $\sqrt{-2}=\sqrt{2}\times\sqrt{-1}=i\sqrt{2}$ (where $i = \sqrt{-1}$). Then we multiply $\sqrt{-2}$ and $\sqrt{3}$. $\sqrt{-2}\times\sqrt{3}=i\sqrt{2\times3}=i\sqrt{6}$

Step3: Combine the results

Multiply the result of step 1 and step 2. $10\times i\sqrt{6}=10i\sqrt{6}$

Answer:

$10i\sqrt{6}$