We will get the simplified expression:
[tex]\sqrt{3}*(5 + \sqrt{24} )\\\\[/tex]
How to simplify the expression?
Here we need to simplify:
[tex]\frac{\sqrt{6} }{\sqrt{3} } - \frac{24}{\sqrt{12} } + 2*\sqrt{48} - 3*\sqrt{8}[/tex]
First, the square root is distributive under product or divisions, then we can rewrite:
[tex]\sqrt{6/2} - \sqrt{\frac{24*24}{12 }} + 2*\sqrt{48} - \sqrt{3^2*8}\\\\\sqrt{3} - \sqrt{48} + 2*\sqrt{48} - \sqrt{72}[/tex]
Where we just distributed the square roots, and we wrote:
3 = √3²
On the ourth term, now finally, what we can do is add the second and third therm to get:
[tex]\sqrt{3} + \sqrt{48} + \sqrt{72}[/tex]
Now, notice that:
48 = 16*3
72 = 24*3
Then we can rewrite:
[tex]\sqrt{3} + \sqrt{3*16} + \sqrt{3*24}\\\\\\\sqrt{3} + \sqrt{3}*\sqrt{16} + \sqrt{3}*\sqrt{24} \\\\\sqrt{3}*(1 + 4 + \sqrt{24} )\\\\\\\sqrt{3}*(5 + \sqrt{24} )\\\\[/tex]
And we can't keep simplifying this.
If you want to learn more about simplifying, you can read:
https://brainly.com/question/723406
