Question

3. Thực hiện phép tính
a) \(\sqrt{51}\):\(\sqrt{117}\)
b) \(\sqrt{2}:\sqrt{7}\)
c) \(\dfrac{3+\sqrt{3}}{\sqrt{2+\sqrt{3}}}\)
d) \(\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right)\) : \(\sqrt{3}\)
e) \(\left(\sqrt{\dfrac{1}{5}}-\sqrt{\dfrac{9}{5}}+\sqrt{5}\right)\): \(\sqrt{5}\)

Answer 1

`sqrt{51} : sqrt{117}`

`= sqrt{51/117}`

`= sqrt{17/39}`

``

`sqrt{2} : sqrt{7}`

`= sqrt{2/7}`

 

Answer 2

`(sqrt{12} + sqrt{27} - sqrt{3}) : sqrt{3}`

`= (2sqrt{3} + 3sqrt{3} - sqrt{3}) : sqrt{3}`

`= 4sqrt{3} : sqrt{3}`

`= 4`

``

`(sqrt{1/5} - sqrt{9/5} + sqrt{5}) : sqrt{5}`

`= (1/sqrt{5} - 3/sqrt{5} + sqrt{5}) : sqrt{5}`

`= (-2/sqrt{5} + sqrt{5}) : sqrt{5}`

`= 1 - 2/5`

`=3/5`