Question

Simplify the expression.

32–√−43–√+62–√+3–√
(1 point)
Responses

−32–√+53–√
negative 3 square root of 2 plus 5 square root of 3

94–√−46–√
9 square root of 4 minus 4 square root of 6

92–√−33–√
9 square root of 2 minus 3 square root of 3

610−−√

Answer 1

To simplify the expression \(32\sqrt{} - 43\sqrt{} + 62\sqrt{} + 3\sqrt{}\), we should first rewrite it clearly:

\[
3\sqrt{2} - 4\sqrt{3} + 6\sqrt{2} + 3\sqrt{1}
\]

Notice that \(3\sqrt{1} = 3\), and it can also represent as \(3\). So the expression can be rearranged as follows:

Combine like terms for \( \sqrt{2} \):

\[
(3\sqrt{2} + 6\sqrt{2}) + (-4\sqrt{3}) + 3
\]
\[
= 9\sqrt{2} - 4\sqrt{3} + 3
\]

So the total result simplifies to:

\[
9\sqrt{2} - 4\sqrt{3} + 3
\]

Now let's check your responses for a match:

**None of the provided responses directly match this result.**

However, among the possible answers provided, it appears:

- \(-3\sqrt{2} + 5\sqrt{3}\)
- \(9\sqrt{4} - 4\sqrt{6}\)
- \(9\sqrt{2} - 3\sqrt{3}\)
- \(6\sqrt{10}\)

**The closest simplification we achieved mathematically was \(9\sqrt{2} - 4\sqrt{3} + 3\), which wasn't in the exact options you provided.**

If you would like a reassessment or new examination based on provided options, please clarify!