Question

(-2 + square root 2)(8 - square root 3)

Answer 1

To simplify the expression \((-2 + \sqrt{2})(8 - \sqrt{3})\), we can use the distributive property (also known as the FOIL method for binomials).

1. Multiply the first terms:
\[ -2 \times 8 = -16 \]

2. Multiply the outer terms:
\[ -2 \times -\sqrt{3} = 2\sqrt{3} \]

3. Multiply the inner terms:
\[ \sqrt{2} \times 8 = 8\sqrt{2} \]

4. Multiply the last terms:
\[ \sqrt{2} \times -\sqrt{3} = -\sqrt{6} \]

Now, combine all these results together:
\[
-16 + 2\sqrt{3} + 8\sqrt{2} - \sqrt{6}
\]

So, the simplified expression is:
\[
-16 + 2\sqrt{3} + 8\sqrt{2} - \sqrt{6}
\]

This is the final form of the expression.