a) \(\sqrt{6+2\sqrt{5}}=\sqrt{5+2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}+1\right)}=\sqrt{5}+1\)
b) \(\sqrt{8-2\sqrt{7}}=\sqrt{7-2\sqrt{7}+1}=\sqrt{\left(\sqrt{7}-1\right)^2}=\sqrt{7}-1\left(do\sqrt{7}>1\right)\)
c) \(\sqrt{9+4\sqrt{5}}=\sqrt{5+2\cdot\sqrt{5}\cdot2+4}=\sqrt{\left(\sqrt{5}+2\right)^2}=2+\sqrt{5}\)
d) \(\sqrt{7-4\sqrt{3}}=\sqrt{4-2\cdot2\cdot\sqrt{3}+3}=\sqrt{\left(2-\sqrt{3}\right)^2}=2-\sqrt{3}\left(do2>\sqrt{3}\right)\)
e) \(\sqrt{8+2\sqrt{15}}=\sqrt{5+2\sqrt{3}\sqrt{5}+3}=\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}=\sqrt{3}+\sqrt{5}\)
g) \(\sqrt{9+4\sqrt{2}}=\sqrt{8+2.\sqrt{8}.1+1}=\sqrt{\left(\sqrt{8}+1\right)^2}=\sqrt{8}+1=2\sqrt{2}+1\)
a) \(\sqrt{6+2\sqrt{5}}=\sqrt{5}+1\)
b) \(\sqrt{8-2\sqrt{7}}=\sqrt{7}-1\)
c) \(\sqrt{9+4\sqrt{5}}=\sqrt{5}+2\)