\(\left(\sqrt{14}+\sqrt{6}\right)\cdot\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{7}+\sqrt{3}\right)\cdot\sqrt{10-2\sqrt{21}}\)
\(=\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
=7-3
=4
chứng minh rằng : (14√14+√12+√30√2+√5).√5−√21=4
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.\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
Viết các biểu thức sau dưới dạng bình phương một tổng hoặc một hiệu :
1) \(5-2\sqrt{6}\)
2) \(8+2\sqrt{15}\)
3) \(10-2\sqrt{21}\)
4) \(21+6\sqrt{6}\)
5) \(14+8\sqrt{3}\)
6) \(36-12\sqrt{5}\)
7) \(25+4\sqrt{6}\)
8) \(98-16\sqrt{3}\)
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 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) \(\sqrt{21-6\sqrt{6}}\)
Tính:
\(\sqrt{54-14\sqrt{5}}-\sqrt{14+6\sqrt{5}}\)
6. √(5+2√6)
7. √(4+2√3)
8. √(4-2√3)
9. √(11-2√30)
10. √(21-4√17)
Tính và rút gọn :
1) \(\sqrt{36+12\sqrt{5}}\)
2) \(\sqrt{21-6\sqrt{6}}\)
3) \(\sqrt{6-2\sqrt{5}}\)\(\:-\sqrt{9-4\sqrt{5}}\)
4) \(\sqrt{3+2\sqrt{2}}\)\(-\sqrt{3-2\sqrt{2}}\)
5) \(\sqrt{4-2\sqrt{3}}\) \(-\sqrt{4+2\sqrt{3}}\)
6) \(\sqrt{6+4\sqrt{2}}\) \(-\sqrt{11-6\sqrt{2}}\)
7) \(\sqrt{21-4\sqrt{5}}\) \(+\sqrt{21+4\sqrt{5}}\)
\(\sqrt{14-6\sqrt[]{}5}\)
