13) \(\sqrt{9+4\sqrt{5}}=\sqrt{2^2+2.2.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(2+\sqrt{5}\right)^2}=2+\sqrt{5}\)
14) \(\sqrt{12+6\sqrt{3}}=\sqrt{3^2+2.3.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(3+\sqrt{3}\right)^2}=3+\sqrt{3}\)
15) \(\sqrt{27-10\sqrt{2}}=\sqrt{5^2-2.5.\sqrt{2}+\left(\sqrt{2}\right)^2}=\sqrt{\left(5-\sqrt{2}\right)^2}=5-\sqrt{2}\)
16) \(\sqrt{18-6\sqrt{5}}=\sqrt{\left(\sqrt{15}\right)^2-2.\sqrt{15}.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(\sqrt{15}-\sqrt{3}\right)^2}=\sqrt{15}-\sqrt{3}\)
17) \(\sqrt{21+4\sqrt{5}}=\sqrt{21+2\sqrt{20}}=\sqrt{\left(\sqrt{20}\right)^2+2\sqrt{20}.1+1^2}\)
\(=\sqrt{\left(\sqrt{20}+1\right)^2}=\sqrt{20}+1\)
18) \(\sqrt{28-6\sqrt{3}}=\sqrt{28-2\sqrt{27}}=\sqrt{\left(\sqrt{27}\right)^2-2\sqrt{27}.1+1^2}\)
\(=\sqrt{\left(\sqrt{27}-1\right)^2}=\sqrt{27}-1\)
19) \(\sqrt{15-10\sqrt{2}}=\sqrt{15-2\sqrt{50}}=\sqrt[]{\left(\sqrt{5}\right)^2-2.\sqrt{5}.\sqrt{10}+\left(\sqrt{10}\right)^2}\)
\(=\sqrt{\left(\sqrt{10}-\sqrt{5}\right)^2}=\sqrt{10}-\sqrt{5}\)
20) \(\sqrt{46-6\sqrt{5}}=\sqrt{46-2\sqrt{45}}=\sqrt{\left(\sqrt{45}\right)^2-2.\sqrt{45}.1+1^2}\)
\(=\sqrt{\left(\sqrt{45}-1\right)^2}=\sqrt{45}-1\)
19) \(\sqrt{12-\sqrt{44}}=\sqrt{12-2\sqrt{11}}=\sqrt{\left(\sqrt{11}\right)^2-2\sqrt{11}.1+1^2}\)
\(=\sqrt{\left(\sqrt{11}-1\right)^2}=\sqrt{11}-1\)
20) \(\sqrt{5-\sqrt{24}}=\sqrt{5-2\sqrt{6}}=\sqrt{\left(\sqrt{3}\right)^2-2.\sqrt{2}.\sqrt{3}+\left(\sqrt{2}\right)^2}\)
\(=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}=\sqrt{3}-\sqrt{2}\)
13: =căn (căn 5+2)^2=căn 5+2
14: =căn (3+căn 3)^2=3+căn 3
15; =căn (5-căn 2)^2=5-căn 2
16: =căn (căn 15-căn 3)^2=căn 15-căn 3
17: =căn (2*căn 5+1)^2=2*căn 5+1
18: =căn (3*căn 3-1)^2=3*căn 3-1
19: =căn 15-2*5căn 2
=căn 15-2*căn 10*căn 5
=căn 10-căn 5
20: =căn (3căn 5-1)^2
=3căn 5-1
18: =căn (căn 7+1)^2=căn 7+1
19: =căn 12-2*căn 11=căn 11-1
17) \(\sqrt{6-\sqrt{20}}=\sqrt{6-2\sqrt{5}}=\sqrt{1^2-2\sqrt{5}.1+\left(\sqrt{5}\right)^2}\)
\(=\sqrt{\left(\sqrt{5}-1\right)^2}=\sqrt{5}-1\)
18) \(\sqrt{8+\sqrt{28}}=\sqrt{8+2\sqrt{7}}=\sqrt{\left(\sqrt{7}\right)^2+2\sqrt{7}+1^2}\)
\(=\sqrt{\left(\sqrt{7}+1\right)^2}=\sqrt{7}+1\)
