Question

Bài 1: Rút gọn biểu thức:

a) \(\dfrac{3+\sqrt{3}}{1+\sqrt{3}}\)

b) \(\dfrac{\sqrt{14}-\sqrt{7}}{2-\sqrt{2}}\)

c) \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)

d) \(\left(2\sqrt{8}+3\sqrt{5}-7\sqrt{2}\right)\left(\sqrt{72}-5\sqrt{20}-2\sqrt{2}\right)\)

Bài 2: So sánh:

a) \(\dfrac{1}{3}\sqrt{6}\) và \(6\sqrt{\dfrac{1}{3}}\)

b) \(\sqrt{15}-\sqrt{14}\) và \(\sqrt{14}-\sqrt{13}\)

c) \(\sqrt{7}-\sqrt{5}\) và  \(\sqrt{5}-\sqrt{3}\)

d) \(\sqrt{105}-\sqrt{101}\) và \(\sqrt{101}-\sqrt{97}\)

Answer 1

Bài `1:`

`a)[3+\sqrt{3}]/[1+\sqrt{3}]=[\sqrt{3}(1+\sqrt{3})]/[1+\sqrt{3}]=\sqrt{3}`

`b)[\sqrt{14}-\sqrt{7}]/[2-\sqrt{2}]=[\sqrt{7}(\sqrt{2}-1)]/[\sqrt{2}(\sqrt{2}-1)]=\sqrt{7}/\sqrt{2}=\sqrt{14}/2`

`c)4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{1/5}`

`=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}.\sqrt{5/5}`

`=8\sqrt{5}-3\sqrt{5}=5\sqrt{5}`

`d)(2\sqrt{8}+3\sqrt{5}-7\sqrt{2})(\sqrt{72}-5\sqrt{20}-2\sqrt{2})`

`=(4\sqrt{2}+3\sqrt{5}-7\sqrt{2})(6\sqrt{2}-10\sqrt{5}-2\sqrt{2})`

`=(3\sqrt{5}-3\sqrt{2})(4\sqrt{2}-10\sqrt{5})`

`=12\sqrt{10}-150-24+30\sqrt{10}`

`=42\sqrt{10}-174`