Rút gọn : Bằng cách bình phương 2 vế H = √((3 + √2)/(3- √2)) - √((3-2√2) / ( 3 + 2√2))

`\text{Đáp án:}`

`\sqrt{{26-2\sqrt{7})/(5+3\sqrt{2}}`

`\text{Giải thích các bước giải:}`

`H=``\sqrt{(3+\sqrt{2})/(3-\sqrt{2})}-\sqrt{(3-2\sqrt{2})/(3+2\sqrt{2})}`

`H^2=``(\sqrt{(3+\sqrt{2})/(3-\sqrt{2})}-\sqrt{(3-2\sqrt{2})/(3+2\sqrt{2})})^2`

`H^2=(\sqrt{(3+\sqrt{2})/(3-\sqrt{2})})^2-2\sqrt{(3+\sqrt{2})/(3-\sqrt{2})}*\sqrt{(3-2\sqrt{2})/(3+2\sqrt{2})}+(\sqrt{(3-2\sqrt{2})/(3+2\sqrt{2})})^2`

`H^2=(3+\sqrt{2})/(3-\sqrt{2})-2\sqrt{(3+\sqrt{2})/(3-\sqrt{2})*(3-2\sqrt{2})/(3+2\sqrt{2})}+(3-2\sqrt{2})/(3+2\sqrt{2})`

`H^2=((3+\sqrt{2})/(3-\sqrt{2})+(3-2\sqrt{2})/(3+2\sqrt{2}))-2\sqrt{(3+\sqrt{2})/(3-\sqrt{2})*(3-2\sqrt{2})/(3+2\sqrt{2})}`

`H^2=((3+\sqrt{2})(3+2\sqrt{2})+(3-2\sqrt{2})(3-\sqrt{2}))/((3-\sqrt{2})(3+2\sqrt{2}))-2\sqrt{((3+\sqrt{2})(3-2\sqrt{2}))/((3-\sqrt{2})(3+2\sqrt{2})`

`H^2=(3^2+6\sqrt{2}+3\sqrt{2}+2(\sqrt{2})^2+3^2-3\sqrt{2}-6\sqrt{2}+2(\sqrt{2})^2)/(3^2+ 6\sqrt{2}-3\sqrt{2}-2(\sqrt{2})^2)-2*\sqrt{3^2-6\sqrt{2}+3\sqrt{2}-2(\sqrt{2})^2}/\sqrt{3^2+6\sqrt{2} -3\sqrt{2}\-2(\sqrt{2} ) ^2`

`H^2=(26)/(5+3\sqrt{2})-(2\sqrt{5-3\sqrt{2}))/(\sqrt{5+3\sqrt{2})`

`H^2=(26-2\sqrt{5-3\sqrt{2})*\sqrt{5+3\sqrt{2}))/(5+3\sqrt{2})`

`H^2=(26-2\sqrt{5^2-(3\sqrt{2})^2))/(5+3\sqrt{2})`

`H^2=(26-2\sqrt{25-18))/(5+3\sqrt{2})`

`H^2=(26-2\sqrt{7})/(5+3\sqrt{2})`

`=>` `H=\sqrt{{26-2\sqrt{7})/(5+3\sqrt{2}}`