![\[ 4\sqrt{4-2\sqrt{3}}+\sqrt{97-56\sqrt{3}} \]](https://latex.artofproblemsolving.com/9/f/d/9fddd85f5503103e4555daf0bdf482050c928b3e.png)
an integer?-
\(4\sqrt{4-2\sqrt{3}}+\sqrt{97-56\sqrt{3}}\)
\(=4\sqrt{3-2\sqrt{3}+1}+\sqrt{49-56\sqrt{3}+48}\)
\(=4\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(7-4\sqrt{3}\right)^2}\)
\(=4\left(\sqrt{3}-1\right)+7-4\sqrt{3}=3\)
So, the value of the expression above is an integer
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