Question

Multiply. Write your answer in simplest form.
(4 + 3 squareroot7) (-squareroot5 - 6 squareroot77)

Answer 1

To multiply \((4 + 3\sqrt{7})(-\sqrt{5} - 6\sqrt{77})\), we will use the distributive property (also known as the FOIL method).

Distributing the terms:

\[
4(-\sqrt{5}) + 4(-6\sqrt{77}) + 3\sqrt{7}(-\sqrt{5}) + 3\sqrt{7}(-6\sqrt{77})
\]

Calculating each term individually:

1. \(4(-\sqrt{5}) = -4\sqrt{5}\)
2. \(4(-6\sqrt{77}) = -24\sqrt{77}\)
3. \(3\sqrt{7}(-\sqrt{5}) = -3\sqrt{35}\)
4. \(3\sqrt{7}(-6\sqrt{77}) = -18\sqrt{539}\)

Now we combine all the results:

\[
-4\sqrt{5} - 24\sqrt{77} - 3\sqrt{35} - 18\sqrt{539}
\]

Thus, the final expression in simplest form is:

\[
\boxed{-4\sqrt{5} - 24\sqrt{77} - 3\sqrt{35} - 18\sqrt{539}}
\]