Question

(- square root 77 - 6square root 22)(3square root 22 + 3square root 33)

Answer 1

To simplify the expression \((- \sqrt{77} - 6\sqrt{22})(3\sqrt{22} + 3\sqrt{33})\), we can use the distributive property (also known as the FOIL method for binomials).

Let's distribute each term from the first parenthesis with each term in the second parenthesis:

1. Distributing \(-\sqrt{77}\):
\[
-\sqrt{77} \cdot 3\sqrt{22} = -3\sqrt{77 \cdot 22} = -3\sqrt{1694}
\]
\[
-\sqrt{77} \cdot 3\sqrt{33} = -3\sqrt{77 \cdot 33} = -3\sqrt{2541}
\]

2. Distributing \(-6\sqrt{22}\):
\[
-6\sqrt{22} \cdot 3\sqrt{22} = -18\sqrt{22 \cdot 22} = -18 \cdot 22 = -396
\]
\[
-6\sqrt{22} \cdot 3\sqrt{33} = -18\sqrt{22 \cdot 33} = -18\sqrt{726}
\]

Now, let's compile all the results together:
\[
(- \sqrt{77} - 6\sqrt{22})(3\sqrt{22} + 3\sqrt{33}) = -3\sqrt{1694} - 3\sqrt{2541} - 396 - 18\sqrt{726}
\]

This is the simplified expression:
\[
-3\sqrt{1694} - 3\sqrt{2541} - 396 - 18\sqrt{726}
\]

If you want numerical approximations or further simplifications, we can proceed with those calculations.