Question

(-5 minus square root of 3) (-2 minus square root of 33)

Answer 1

To simplify the expression \((-5 - \sqrt{3})(-2 - \sqrt{33})\), we can use the distributive property (also known as the FOIL method for binomials):

1. **First**: Multiply the first terms:
\[
(-5) \times (-2) = 10
\]

2. **Outer**: Multiply the outer terms:
\[
(-5) \times (-\sqrt{33}) = 5\sqrt{33}
\]

3. **Inner**: Multiply the inner terms:
\[
(-\sqrt{3}) \times (-2) = 2\sqrt{3}
\]

4. **Last**: Multiply the last terms:
\[
(-\sqrt{3}) \times (-\sqrt{33}) = \sqrt{3} \times \sqrt{33} = \sqrt{99} = 3\sqrt{11}
\]

Now, combine all these results:
\[
10 + 5\sqrt{33} + 2\sqrt{3} + 3\sqrt{11}
\]

So the final result is:
\[
10 + 5\sqrt{33} + 2\sqrt{3} + 3\sqrt{11}
\]