Question

rút gọn biểu thức

Answer 1

`(sqrt{24}+sqrt{75}-3)/(2sqrt{14}+sqrt{175}-sqrt{21})`

`=(sqrt3(sqrt8+sqrt25-sqrt3))/(sqrt7(2sqrt2+sqrt{25}-sqrt3))`

`=sqrt3/sqrt7`

`=sqrt{3/7}`

`**sqrt8=sqrt{4.2}=2sqrt2`

Answer 2

\(\dfrac{\sqrt{24}+\sqrt{75}-3}{2\sqrt{14}+\sqrt{175}-\sqrt{21}}=\dfrac{2\sqrt{3}.\sqrt{2}+5\sqrt{3}-3}{2\sqrt{2}.\sqrt{7}+5\sqrt{7}-\sqrt{3}.\sqrt{7}}\)

\(=\dfrac{\sqrt{3}\left(2\sqrt{2}+5-\sqrt{3}\right)}{\sqrt{7}\left(2\sqrt{2}+5-\sqrt{3}\right)}=\dfrac{\sqrt{3}}{\sqrt{7}}=\dfrac{\sqrt{21}}{7}\)

Answer 3

Ta có: \(\dfrac{\sqrt{24}+\sqrt{75}-3}{2\sqrt{14}+\sqrt{175}-\sqrt{21}}\)

\(=\dfrac{\sqrt{3}\left(2\sqrt{2}+5-\sqrt{3}\right)}{\sqrt{7}\left(2\sqrt{2}+5-\sqrt{3}\right)}=\dfrac{\sqrt{21}}{7}\)