Question

(3 - square root 3)(-9 + 7square root 22)

Answer 1

To simplify the expression \((3 - \sqrt{3})(-9 + 7\sqrt{22})\), we will use the distributive property (also known as the FOIL method for binomials).

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

\[
(3 - \sqrt{3})(-9 + 7\sqrt{22}) = 3 \cdot (-9) + 3 \cdot (7\sqrt{22}) - \sqrt{3} \cdot (-9) - \sqrt{3} \cdot (7\sqrt{22})
\]

Now, calculate each term:

1. \(3 \cdot (-9) = -27\)
2. \(3 \cdot (7\sqrt{22}) = 21\sqrt{22}\)
3. \(-\sqrt{3} \cdot (-9) = 9\sqrt{3}\)
4. \(-\sqrt{3} \cdot (7\sqrt{22}) = -7\sqrt{66}\) (since \(\sqrt{3} \cdot \sqrt{22} = \sqrt{66}\))

Now we can combine these results:

\[
-27 + 21\sqrt{22} + 9\sqrt{3} - 7\sqrt{66}
\]

Thus, the simplified expression is:

\[
-27 + 21\sqrt{22} + 9\sqrt{3} - 7\sqrt{66}
\]