Question

negative square root of 5 (9 + square root of 10)
Multiply. Write your answer in simplest form.

Answer 1

To multiply the expression \(-\sqrt{5} (9 + \sqrt{10})\), we can distribute \(-\sqrt{5}\) to both terms within the parentheses.

The calculation proceeds as follows:

\[
-\sqrt{5} \cdot 9 + (-\sqrt{5}) \cdot \sqrt{10}
\]

1. For the first term:
\[
-\sqrt{5} \cdot 9 = -9\sqrt{5}
\]

2. For the second term:
\[
-\sqrt{5} \cdot \sqrt{10} = -\sqrt{5 \cdot 10} = -\sqrt{50}
\]
We can simplify \(\sqrt{50}\):
\[
\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}
\]
Thus, the second term becomes:
\[
-\sqrt{50} = -5\sqrt{2}
\]

Now we combine both results:
\[
-9\sqrt{5} - 5\sqrt{2}
\]

Therefore, the final answer in simplest form is:
\[
\boxed{-9\sqrt{5} - 5\sqrt{2}}
\]