\(1,4-2\sqrt{3}=\left(\sqrt{3}-1\right)^2\\ 2,\sqrt{7-4\sqrt{3}}=\sqrt{\left(2-\sqrt{3}\right)^2}=2-\sqrt{3}\\ 3,\sqrt{5+2\sqrt{6}}=\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}=\sqrt{2}+\sqrt{3}\\ 4,\sqrt{16+6\sqrt{7}}=\sqrt{\left(3+\sqrt{7}\right)^2}=3+\sqrt{7}\\ 5,\sqrt{12+2\sqrt{35}}=\sqrt{\left(\sqrt{7}+\sqrt{5}\right)^2}=\sqrt{7}+\sqrt{5}\\ 6,\sqrt{9-4\sqrt{5}}=\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}-2\)
Tick plzzz
1. \(\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)
2. \(\sqrt{7-4\sqrt{3}}=\sqrt{\left(2-\sqrt{3}\right)^2}=2-\sqrt{3}\)
3. \(\sqrt{5+2\sqrt{6}}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}=\sqrt{3}+\sqrt{2}\)
4. \(\sqrt{16+6\sqrt{7}}=\sqrt{\left(3+\sqrt{7}\right)^2}=3+\sqrt{7}\)
5. \(\sqrt{12+2\sqrt{35}}=\sqrt{\left(\sqrt{7}+\sqrt{5}\right)^2}=\sqrt{7}+\sqrt{5}\)
6. \(\sqrt{9-4\sqrt{5}}=\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}-2\)
7. \(\sqrt{18-2\sqrt{65}}=\sqrt{\left(\sqrt{13}-\sqrt{5}\right)^2}=\sqrt{13}-\sqrt{5}\)
8. \(\sqrt{27+10\sqrt{2}}=\sqrt{\left(5+\sqrt{2}\right)^2}=5+\sqrt{2}\)
9. \(\sqrt{14+6\sqrt{5}}=\sqrt{\left(3+\sqrt{5}\right)^2}=3+\sqrt{5}\)
10. \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}=\sqrt{\left(1+\sqrt{2}\right)^2}-\sqrt{\left(2-\sqrt{2}\right)^2}=1+\sqrt{2}-2+\sqrt{2}=2\sqrt{2}-1\)
11. \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}=2\sqrt{2}\)
12. \(\sqrt{3+2\sqrt{2}}+\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{\left(1+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=1+\sqrt{2}+\sqrt{3}-\sqrt{2}=1+\sqrt{3}\)
13. \(\sqrt{9-4\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
\(=\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(\sqrt{5}+1\right)^2}\)
\(=\sqrt{5}-2+\sqrt{5}+1=2\sqrt{5}-1\)
14. \(\sqrt{11+6\sqrt{2}}+\sqrt{6+4\sqrt{2}}-2\sqrt{2}\)
\(=\sqrt{\left(3+\sqrt{2}\right)^2}+\sqrt{\left(2+\sqrt{2}\right)^2}-2\sqrt{2}\)
\(=3+\sqrt{2}+2+\sqrt{2}-2\sqrt{2}=5\)
15. \(\sqrt{15-6\sqrt{6}}+\sqrt{10+4\sqrt{6}}-\sqrt{7+2\sqrt{6}}\)
\(=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(2+\sqrt{6}\right)^2}-\sqrt{\left(1+\sqrt{6}\right)^2}\)
\(=3-\sqrt{6}+2+\sqrt{6}-1-\sqrt{6}=4-\sqrt{6}\)
16. \(\sqrt{31-8\sqrt{15}}+\sqrt{24-6\sqrt{15}}\)
\(=\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{\left(\sqrt{15}-3\right)^2}\)
\(=4-\sqrt{15}+\sqrt{15}-3=1\)
1: \(\sqrt{4-2\sqrt{3}}=\sqrt{3}-1\)
2: \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)
3: \(\sqrt{5+2\sqrt{6}}=\sqrt{3}+\sqrt{2}\)
4: \(\sqrt{16+6\sqrt{7}}=3+\sqrt{7}\)
5: \(\sqrt{12+2\sqrt{35}}=\sqrt{7}+\sqrt{5}\)
6: \(\sqrt{9-4\sqrt{5}}=\sqrt{5}-2\)
7: \(\sqrt{18-2\sqrt{65}}=\sqrt{13}-\sqrt{5}\)
8: \(\sqrt{27+10\sqrt{2}}=5+\sqrt{2}\)
9: \(\sqrt{14+6\sqrt{5}}=3+\sqrt{5}\)
10: \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
\(=\sqrt{2}+1-2+\sqrt{2}\)
\(=2\sqrt{2}-1\)
11: \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}\)
\(=2\sqrt{2}\)
12: \(\sqrt{3+2\sqrt{2}}+\sqrt{5-2\sqrt{6}}\)
\(=\sqrt{2}+1+\sqrt{3}-\sqrt{2}\)
\(=\sqrt{3}+1\)
13: \(\sqrt{9-4\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
\(=\sqrt{5}-2+\sqrt{5}+1\)
\(=2\sqrt{5}-1\)
14: \(\sqrt{11+6\sqrt{2}}+\sqrt{6+4\sqrt{2}}-2\sqrt{2}\)
\(=3+\sqrt{2}+2+\sqrt{2}-2\sqrt{2}\)
=5
15: \(\sqrt{15-6\sqrt{6}}+\sqrt{10+4\sqrt{6}}-\sqrt{7+2\sqrt{6}}\)
\(=3-\sqrt{6}+\sqrt{6}+2-\sqrt{6}-1\)
\(=4-\sqrt{6}\)
16: \(\sqrt{31-8\sqrt{15}}+\sqrt{24-6\sqrt{15}}\)
\(=4-\sqrt{15}+\sqrt{15}-3\)
=1
