Question

Tính giá trị của các biểu thức sau:

a) \(\left(\sqrt{99}-\sqrt{18}+\sqrt{11}\right)\times\sqrt{11}+3\sqrt{22}\)

b) \(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)

c) \(\dfrac{5}{\sqrt{7}+\sqrt{2}}-\dfrac{7-\sqrt{7}}{\sqrt{7}-1}+6\sqrt{\dfrac{1}{2}}\)

Answer 1

a: \(=\left(3\sqrt{11}+\sqrt{11}-\sqrt{18}\right)\cdot\sqrt{11}+3\sqrt{22}\)

\(=44-\sqrt{198}+\sqrt{198}=44\)

b: \(=\sqrt{3}+1+\sqrt{3}-1=2\sqrt{3}\)

c: \(=\sqrt{7}-\sqrt{2}-\sqrt{7}+3\sqrt{2}=2\sqrt{2}\)

Answer 2

`(a):\  (\sqrt{99}-\sqrt{18}+\sqrt{11}).\sqrt{11}+3\sqrt{22}`

`=(\sqrt{9}.\sqrt{11}-\sqrt{9}.\sqrt{2}+\sqrt{11}).\sqrt{11}+3\sqrt{22}`

`=3.\sqrt{11}^{2}-3.\sqrt{2}.\sqrt{11}+\sqrt{11}^{2}+3\sqrt{22}`

`=3.11-3.\sqrt{22}+11+3\sqrt{22}`

`=33+11=44`

`(b):\  \sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}`

`=\sqrt{3+2\sqrt{3}+1}+\sqrt{3-2\sqrt{3}+1}`

`=\sqrt{(\sqrt{3}+1)^{2}}+\sqrt{(\sqrt{3}-1)^{2}}`

`=|\sqrt{3}+1|+|\sqrt{3}-1|`

`=\sqrt{3}+1+\sqrt{3}-1`

`=2\sqrt{3}`

`(c):\  (5)/(\sqrt{7}+\sqrt{2})-(7-\sqrt{7})/(\sqrt{7}-1)+6\sqrt{1/2}`

`=(5(\sqrt{7}-\sqrt{2}))/((\sqrt{7}-\sqrt{2})(\sqrt{7}+\sqrt{2}))-(\sqrt{7}(\sqrt{7}-1))/(\sqrt{7}-1)+(6)/(\sqrt{2})`

`=(5(\sqrt{7}-\sqrt{2}))/(7-2)-\sqrt{7}+(6\sqrt{2})/(2)`

`=\sqrt{7}-\sqrt{2}-\sqrt{7}+3\sqrt{2}`

`=2\sqrt{2}`