Question

(-8 - 7square root 3)(6 + square root 7)

Answer 1

To simplify the expression \((-8 - 7\sqrt{3})(6 + \sqrt{7})\), we can use the distributive property (also known as the FOIL method for binomials):

\[
(-8)(6) + (-8)(\sqrt{7}) + (-7\sqrt{3})(6) + (-7\sqrt{3})(\sqrt{7})
\]

Now, let's compute each term:

1. \((-8)(6) = -48\)
2. \((-8)(\sqrt{7}) = -8\sqrt{7}\)
3. \((-7\sqrt{3})(6) = -42\sqrt{3}\)
4. \((-7\sqrt{3})(\sqrt{7}) = -7\sqrt{21}\) (since \(\sqrt{3} \cdot \sqrt{7} = \sqrt{21}\))

Now, let's combine these results:

\[
-48 - 8\sqrt{7} - 42\sqrt{3} - 7\sqrt{21}
\]

This cannot be simplified any further because the terms involve different radicals and constants. Thus, the final simplified result is:

\[
-48 - 8\sqrt{7} - 42\sqrt{3} - 7\sqrt{21}
\]