Multiply nine root of 3-6 square root of seven give an exact number

To multiply \( 9\sqrt{3} \) and \( 6\sqrt{7} \), you can use the following steps:

1. Multiply the coefficients (the numbers in front of the square roots).
2. Multiply the square roots.

So, it looks like this:

\[
(9\sqrt{3})(6\sqrt{7}) = (9 \times 6)(\sqrt{3} \times \sqrt{7})
\]

Calculating the coefficients:

\[
9 \times 6 = 54
\]

Now, multiplying the square roots:

\[
\sqrt{3} \times \sqrt{7} = \sqrt{21}
\]

Putting it all together, we get:

\[
9\sqrt{3} \times 6\sqrt{7} = 54\sqrt{21}
\]

Thus, the exact result is:

\[
54\sqrt{21}
\]