Question

(square root 22 - 10square root 21)(-9 + square root 2)

Answer 1

To simplify the expression \((\sqrt{22} - 10\sqrt{21})(-9 + \sqrt{2})\), we'll distribute each term in the first parenthesis by each term in the second parenthesis.

Let's break it down step-by-step:

1. **Distribute \(\sqrt{22}\)**:
\[
\sqrt{22} \cdot (-9) + \sqrt{22} \cdot \sqrt{2}
\]
This gives us:
\[
-9\sqrt{22} + \sqrt{44}
\]

Since \(\sqrt{44} = \sqrt{4 \cdot 11} = 2\sqrt{11}\), we have:
\[
-9\sqrt{22} + 2\sqrt{11}
\]

2. **Distribute \(-10\sqrt{21}\)**:
\[
-10\sqrt{21} \cdot (-9) + (-10\sqrt{21}) \cdot \sqrt{2}
\]
This gives us:
\[
90\sqrt{21} - 10\sqrt{42}
\]

3. **Combine all the terms**:
Putting it all together, we have:
\[
-9\sqrt{22} + 2\sqrt{11} + 90\sqrt{21} - 10\sqrt{42}
\]

So, the simplified expression is:
\[
-9\sqrt{22} + 2\sqrt{11} + 90\sqrt{21} - 10\sqrt{42}
\]