Rút gọn các biểu thức sau
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Bài 1. Rút gọn các biểu thức sau:
1) \( \sqrt{72} + \frac{1}{2} \sqrt{32} - \sqrt{162} ; \)
2) \( \frac{1}{2} \sqrt{48} - 2\sqrt{75} - \frac{\sqrt{33}}{\sqrt{11}} + 5\sqrt{\frac{1}{3}} ; \)
3) \( \frac{2\sqrt{3} - \sqrt{6} - \sqrt{216}}{\sqrt{8}-2} \cdot \frac{1}{\sqrt{6}} ; \)
4) \( \left( \frac{1}{\sqrt{5} - \sqrt{2}} + \frac{1}{\sqrt{5} + \sqrt{2}} \right) \cdot \frac{1}{(\sqrt{2}+1)^{2}} ; \)
5) \( \left( \frac{15}{\sqrt{6}+1} + \frac{4}{\sqrt{3}-\sqrt{6}} - \frac{12}{3-\sqrt{6}} \right) \cdot \sqrt{(6+11)} ; \)
6) \( \left( 1 - \frac{5 - \sqrt{5}}{1+\sqrt{5}} \right) \left( \frac{5}{1 - \sqrt{5}} \right) ; \)
7) \( \frac{3 + 2\sqrt{3}}{\sqrt{3}} + \frac{2 + \sqrt{2}}{2 + 1} - \sqrt{2 + \sqrt{3}} ; \)
8) \( \left( \frac{\sqrt{14} - \sqrt{7}}{1 - \sqrt{2}} + \frac{\sqrt{15} - \sqrt{5}}{1 - \sqrt{3}} \right) \cdot \frac{1}{\sqrt{7} - \sqrt{5}} ; \)
9) \( \left( \frac{3}{2}\sqrt{6} + 2\sqrt{\frac{2}{4}} - \frac{3}{2} \sqrt{2} \right) \left( \frac{3}{2}\sqrt{3} - \sqrt{12 - \sqrt{6}} \right) ; \)
10) \( \left( \frac{1}{\sqrt{7} - \sqrt{3}} \cdot \frac{1}{\sqrt{7} + \sqrt{3}} \right) \cdot \frac{1}{(\sqrt{3}+1)} ; \)
11) \( \left( \sqrt{2}+1 \right)^{3} \cdot \left( \sqrt{4-\sqrt{2}+1} \right) ; \)
12) \( \sqrt{5}+1)^{3}-3\sqrt{5+1} ; \)
13) \( \sqrt{26}+15\sqrt{4-\sqrt{26}-15} ; \)
14) \( \sqrt{20+14\sqrt{2}} + \sqrt{20-14\sqrt{2}} .\)
Bài 1. Rút gọn các biểu thức sau:
1) \( \sqrt{72} + \frac{1}{2} \sqrt{32} - \sqrt{162} ; \)
2) \( \frac{1}{2} \sqrt{48} - 2\sqrt{75} - \frac{\sqrt{33}}{\sqrt{11}} + 5\sqrt{\frac{1}{3}} ; \)
3) \( \frac{2\sqrt{3} - \sqrt{6} - \sqrt{216}}{\sqrt{8}-2} \cdot \frac{1}{\sqrt{6}} ; \)
4) \( \left( \frac{1}{\sqrt{5} - \sqrt{2}} + \frac{1}{\sqrt{5} + \sqrt{2}} \right) \cdot \frac{1}{(\sqrt{2}+1)^{2}} ; \)
5) \( \left( \frac{15}{\sqrt{6}+1} + \frac{4}{\sqrt{3}-\sqrt{6}} - \frac{12}{3-\sqrt{6}} \right) \cdot \sqrt{(6+11)} ; \)
6) \( \left( 1 - \frac{5 - \sqrt{5}}{1+\sqrt{5}} \right) \left( \frac{5}{1 - \sqrt{5}} \right) ; \)
7) \( \frac{3 + 2\sqrt{3}}{\sqrt{3}} + \frac{2 + \sqrt{2}}{2 + 1} - \sqrt{2 + \sqrt{3}} ; \)
8) \( \left( \frac{\sqrt{14} - \sqrt{7}}{1 - \sqrt{2}} + \frac{\sqrt{15} - \sqrt{5}}{1 - \sqrt{3}} \right) \cdot \frac{1}{\sqrt{7} - \sqrt{5}} ; \)
9) \( \left( \frac{3}{2}\sqrt{6} + 2\sqrt{\frac{2}{4}} - \frac{3}{2} \sqrt{2} \right) \left( \frac{3}{2}\sqrt{3} - \sqrt{12 - \sqrt{6}} \right) ; \)
10) \( \left( \frac{1}{\sqrt{7} - \sqrt{3}} \cdot \frac{1}{\sqrt{7} + \sqrt{3}} \right) \cdot \frac{1}{(\sqrt{3}+1)} ; \)
11) \( \left( \sqrt{2}+1 \right)^{3} \cdot \left( \sqrt{4-\sqrt{2}+1} \right) ; \)
12) \( \sqrt{5}+1)^{3}-3\sqrt{5+1} ; \)
13) \( \sqrt{26}+15\sqrt{4-\sqrt{26}-15} ; \)
14) \( \sqrt{20+14\sqrt{2}} + \sqrt{20-14\sqrt{2}} .\)