Đáp án`+`Giải thích các bước giải:
`a)` $\sqrt{4 + 2\sqrt{3}}$
`=` $\sqrt{3 + 2\sqrt{3} + 1 }$
`=` $\sqrt{(\sqrt{3}+1)^2}$
` = |` $\sqrt{3}$ `+1`|
`=` $\sqrt{3}$ `+1`
` b)` $\sqrt{9 + 4\sqrt{5}}$
`=` $\sqrt{5 + 4 -2.2 + \sqrt{5}}$
`=` $\sqrt{(\sqrt{5}-2)^2}$
`= | ` $\sqrt{5}$ `-2` `|`
`=` $\sqrt{5}$ `-2`
` c)` $\sqrt{8 - 2\sqrt{15}}$
`=` $\sqrt{(\sqrt{5})^2 + 2 . \sqrt{5} . \sqrt{3} + (\sqrt{3})^2}$
`=` $\sqrt{(\sqrt{5} + \sqrt{3})^2}$
`= | ` $\sqrt{5}$ `+` $\sqrt{3}$ `|`
`=` $\sqrt{5}$ `+` $\sqrt{3}$
` d) ` $\sqrt{6 + 2\sqrt{5}}$ `-` $\sqrt{6 - 2\sqrt{5}}$
`=` $\sqrt{(\sqrt{5})^2 + 2.\sqrt{5}.\sqrt{1} + 1}$ `-` $\sqrt{(\sqrt{5})^2 - 2.\sqrt{5}.\sqrt{1} + 1}$
`=` $\sqrt{(\sqrt{5} + 1)^2}$ `-` $\sqrt{(\sqrt{5} - 1)^2}$
`=` `|` $\sqrt{5}$ `+` `1` `|` `-` `|` $\sqrt{5}$ `+` `1` `|`
`=` $\sqrt{5}$ `+ 1` `-` $\sqrt{5}$ `+1`
`= 2`
` e) ` $\sqrt{7 + \sqrt{13}}$ `-` $\sqrt{7 - \sqrt{13}}$
Đặt bt là `A`
Nhân căn `2` cho `2` vế , ta đc `:`
`-> √2A = ` $\sqrt{2}$`.` $\sqrt{7 + \sqrt{13}}$ `-` $\sqrt{2}$`.`$\sqrt{7 - \sqrt{13}}$
`=` $\sqrt{\sqrt{2} .( 7 + \sqrt{13})}$ `-` $\sqrt{\sqrt{2}.( 7 - \sqrt{13})}$
`=` $\sqrt{14 + 2\sqrt{3}}$ `-` $\sqrt{14 - 2\sqrt{3}}$
`=` $\sqrt{(\sqrt{13}+1)^2}$ `-` $\sqrt{(\sqrt{13} - 1)^2}$
`=` `|` $\sqrt{13}$ `+1` `|` `-` `|` $\sqrt{13}$ `-` `1|`
`=` $\sqrt{13}$ `+1 ` `- ` $\sqrt{13}$ `+1`
`=2`
`-> A = 2 : ` $\sqrt{2}$
`= ` $\sqrt{2}$
