Question

(4 - 9square root 55) (-10 + square root 11)

Answer 1

To multiply the two expressions \((4 - 9\sqrt{55})\) and \((-10 + \sqrt{11})\), we can use the distributive property (also known as the FOIL method for binomials).

Let's distribute each term in the first expression by each term in the second expression:

\[
(4 - 9\sqrt{55})(-10 + \sqrt{11})
\]

Calculating each pair of products, we have:

1. \(4 \times -10 = -40\)
2. \(4 \times \sqrt{11} = 4\sqrt{11}\)
3. \(-9\sqrt{55} \times -10 = 90\sqrt{55}\)
4. \(-9\sqrt{55} \times \sqrt{11} = -9 \sqrt{605}\) (since \(\sqrt{55} \cdot \sqrt{11} = \sqrt{55 \times 11} = \sqrt{605}\))

Now, combining these results:

\[
-40 + 4\sqrt{11} + 90\sqrt{55} - 9\sqrt{605}
\]

Therefore, the final result of the multiplication is:

\[
-40 + 4\sqrt{11} + 90\sqrt{55} - 9\sqrt{605}
\]