Question

(4 - square root 2)(6 - 3square root 3)

Answer 1

To simplify the expression \((4 - \sqrt{2})(6 - 3\sqrt{3})\), we can use the distributive property (also known as the FOIL method for binomials).

Let's multiply each term in the first binomial by each term in the second binomial:

\[
(4 - \sqrt{2})(6 - 3\sqrt{3}) = 4 \cdot 6 + 4 \cdot (-3\sqrt{3}) - \sqrt{2} \cdot 6 - \sqrt{2} \cdot (-3\sqrt{3})
\]

Calculating each term:

1. \(4 \cdot 6 = 24\)
2. \(4 \cdot (-3\sqrt{3}) = -12\sqrt{3}\)
3. \(-\sqrt{2} \cdot 6 = -6\sqrt{2}\)
4. \(-\sqrt{2} \cdot (-3\sqrt{3}) = 3\sqrt{6}\)

Now, we combine all the terms:

\[
24 - 12\sqrt{3} - 6\sqrt{2} + 3\sqrt{6}
\]

So, the final simplified expression is:

\[
\boxed{24 - 12\sqrt{3} - 6\sqrt{2} + 3\sqrt{6}}
\]