Question

Simplify : root 6 plus 2 root 3 minus 6 root 3 plus 3.

Answer 1

To simplify the expression \(\sqrt{6} + 2\sqrt{3} - 6\sqrt{3} + 3\), we start by combining the like terms.

1. Combine the constant terms:
\[
3
\]

2. Combine the terms involving \(\sqrt{3}\):
\[
2\sqrt{3} - 6\sqrt{3} = -4\sqrt{3}
\]

3. Now, rewrite the entire expression by combining all these parts:
\[
\sqrt{6} + (-4\sqrt{3}) + 3
\]
This can be rearranged as:
\[
\sqrt{6} - 4\sqrt{3} + 3
\]

Thus, the simplified expression is:
\[
\sqrt{6} - 4\sqrt{3} + 3
\]

Alternatively, we can also express it as:
\[
\sqrt{6} + 3 - 4\sqrt{3}
\]

This is the simplified form.