Question

[ngoc tranbao]

14. √(7-4√3)

15. √(8+2√15)

16. √(10-2√21)

17. √(11+2√18)

18. √(7+2√10)

19. √(7+4√3)

20. √(12-2√35)

Answer 1

[Nguyễn Lê Phước Thịnh]

14) \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)

15) \(\sqrt{8+2\sqrt{15}}=\sqrt{5}+\sqrt{3}\)

16) \(\sqrt{10-2\sqrt{21}}=\sqrt{7}-\sqrt{3}\)

17) \(\sqrt{11+2\sqrt{18}}=3+\sqrt{2}\)

18) \(\sqrt{7+2\sqrt{10}}=\sqrt{5}+\sqrt{2}\)

19) \(\sqrt{7+4\sqrt{3}}=2+\sqrt{3}\)

20) \(\sqrt{12-2\sqrt{35}}=\sqrt{7}-\sqrt{5}\)

Answer 2

[An Thy]

\(\sqrt{7-4\sqrt{3}}=\sqrt{2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(2-\sqrt{3}\right)^2}=\left|2-\sqrt{3}\right|=2-\sqrt{3}\)