Answer:
Step-by-step explanation:
[tex]\displaystyle \Large \boldsymbol{} 5\cdot \sqrt{3:2\sqrt{3-\sqrt{2} } } =\\\\\\ 5\cdot \sqrt{\frac{3}{2\sqrt{3-\sqrt{2} } } \cdot \frac{2\sqrt{3+\sqrt{2} } }{2\sqrt{3+\sqrt{2} } } } = \\\\\\5\cdot \sqrt{\frac{6\sqrt{3+\sqrt{2} } }{4\cdot \sqrt{9-2} } } =5\sqrt{\frac{6\sqrt{3+\sqrt{2} } }{2\sqrt{7} } }[/tex]
But if the condition would be like this
[tex]\displaystyle \Large \boldsymbol{} 5\cdot \sqrt{3:2\sqrt{3-\boldsymbol2\sqrt{2} } } =\\\\\\5\cdot \sqrt{\frac{3}{2\cdot \sqrt{\underbrace{2+1-2\sqrt{2} \cdot \sqrt{1} }_{(\sqrt{2} -1)^2} } }} =\\\\\\5\cdot \sqrt{\frac{3}{2\cdot (\sqrt{2}-1) } } } = \\\\\\ 5\cdot \sqrt{\frac{3}{2(\sqrt{2}-1 )} \cdot \frac{\sqrt{2} +1}{\sqrt{2}+1 }} =5 \sqrt{\frac{3}{2(2-1)} } =\boxed{5\sqrt{1,5} }[/tex]
