Ta có : \(\sqrt{54-14\sqrt{5}}-\sqrt{14+6\sqrt{5}}\)
\(=\sqrt{7^2-2.7.\sqrt{5}+\left(\sqrt{5}\right)^2}-\sqrt{3^2+2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}\)
\(=\sqrt{\left(7-\sqrt{5}\right)^2}-\sqrt{\left(3+\sqrt{5}\right)^2}\)
\(=7-\sqrt{5}-\left(3+\sqrt{5}\right)=7-\sqrt{5}-3-\sqrt{5}=4\)
1.
a) \(\sqrt{24-4\sqrt{5}}+\sqrt{14-6\sqrt{5}}\)
b)\(\sqrt{31-12\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)
1.\(\sqrt{\frac{129}{16}+\sqrt{2}}\)
2.\(\sqrt{\frac{289+4\sqrt{72}}{16}}\)
3. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
4.\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
5.\(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
6.\(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4-\sqrt{15}}\)
7.\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
\(\sqrt{14-6\sqrt[]{}5}\)
Tính
a.\(\sqrt{8+2\sqrt{5}}\) b.\(\sqrt{10-2\sqrt[]{5}}\) c.\(\sqrt{5+\sqrt{24}}\) d.\(\sqrt{12-\sqrt{140}}\)
e.\(\sqrt{14+2\sqrt{5}}\) f. \(\sqrt{8-\sqrt{28}}\) g.\(\sqrt{23-4\sqrt{15}}\) h.\(\sqrt{9+4\sqrt{2}}\)
giúp mik vs mai mik nộp rồi,cảm ơn mn nhiều
Tính và rút gọn :
1) \(\sqrt{14+2\sqrt{33}}\)
2) \(\sqrt{29-12\sqrt{5}}\)
3) \(\sqrt{16+2\sqrt{55}}\)
4) \(\sqrt{13+4\sqrt{10}}\)
5) \(\sqrt{36+12\sqrt{5}}\)
6) \(\sqrt{21-6\sqrt{6}}\)
Rút gọn biểu thức
a) \(\sqrt{11-2\sqrt{10}}\)
b) \(\sqrt{9-2\sqrt{14}}\)
c) \(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
d) \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
e) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
g) \(\sqrt{3}+\sqrt{11+6\sqrt{2}}+\sqrt{5+2\sqrt{6}}\)
h) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
k) \(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)
i) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
\(\left(\sqrt{2}-\sqrt{7}\right)-5\sqrt{9+2\sqrt{14}}\)
1,\(\sqrt{14+8\sqrt{3}}\)
2, \(\sqrt{14+4\sqrt{10}}\)
3, \(\sqrt{21+6\sqrt{6}}\)
4, \(\sqrt{13-4\sqrt{10}}\)
Tính:
a/ \(\sqrt{8+2\sqrt{15}}+\frac{2}{\sqrt{5}+\sqrt{3}}\)
b/ \(\sqrt{7+2\sqrt{6}}+\frac{6-2\sqrt{6}}{\sqrt{6}}-\sqrt{54}\)
