Question

(6 - square root 5)(-3 -9square root 6)

Answer 1

To simplify the expression \((6 - \sqrt{5})(-3 - 9\sqrt{6})\), we will use the distributive property (also known as the FOIL method for binomials).

Let's expand it step by step:

\[
(6 - \sqrt{5})(-3 - 9\sqrt{6}) = 6 \cdot (-3) + 6 \cdot (-9\sqrt{6}) - \sqrt{5} \cdot (-3) - \sqrt{5} \cdot (-9\sqrt{6})
\]

Now, calculate each term:

1. \(6 \cdot (-3) = -18\)
2. \(6 \cdot (-9\sqrt{6}) = -54\sqrt{6}\)
3. \(-\sqrt{5} \cdot (-3) = 3\sqrt{5}\)
4. \(-\sqrt{5} \cdot (-9\sqrt{6}) = 9\sqrt{30}\) (since \(\sqrt{5} \cdot \sqrt{6} = \sqrt{30}\))

Now, combine all the results:

\[
-18 - 54\sqrt{6} + 3\sqrt{5} + 9\sqrt{30}
\]

So, the final expression is:

\[
-18 - 54\sqrt{6} + 3\sqrt{5} + 9\sqrt{30}
\]

This is the simplified form of \((6 - \sqrt{5})(-3 - 9\sqrt{6})\).