[tex]The\ product\ of 3 \sqrt{8}*4 \sqrt{3}\ is\ 24 \sqrt{6}.[/tex]
First, recognize that all the numbers can be moved around because they are being multiplied together.
Next, rearrange the expression so that the whole-number coefficients are together:
[tex]3\sqrt{8}*4\sqrt{6}[/tex]
[tex]3*4*\sqrt{8}*\sqrt{3}[/tex]
Now try to simplify the square-roots to find any squares inside that can be reduced and taken out of the square-root:
[tex]3*4*\sqrt{(2*2*2)}*\sqrt{3}[/tex]
[tex]3*4*\sqrt{4*2}*\sqrt{3}[/tex]
Multiply the square roots together:
[tex]3*4*\sqrt{(4*2*3)}[/tex]
[tex]3*4*\sqrt{(4*6)}[/tex]
Now take out the square-root of 4 and simplify
[tex]3*4*\sqrt{4}*\sqrt{6}[/tex]
[tex]3*4*(2)*\sqrt{6}[/tex]
[tex]24\sqrt{6}[/tex]
[tex]Thus,\ your\ answer\ is\ 24\sqrt{6}[/tex]
