Giải thích các bước giải:

a) $3\sqrt{12}+\sqrt{7,5}.\sqrt{10}-3\sqrt{\dfrac{100}{3}}$

$=6\sqrt 3+\sqrt{75}-\sqrt{9.\dfrac{100}{3}}$

$=6\sqrt 3+5\sqrt 3-10\sqrt 3$

$=\sqrt 3$

b) $\sqrt{(\sqrt 6-2)^2}+\sqrt{15-6\sqrt 6}$

$=|\sqrt 6-2|+\sqrt{9-2.3.\sqrt 6+6}$

$=\sqrt 6-2+\sqrt{(3-\sqrt{6})^2}$

$=\sqrt 6-2+|3-\sqrt 6|$

$=\sqrt 6-2+3-\sqrt 6$

$=1$

c) $\dfrac{2\sqrt 3-\sqrt 6}{\sqrt 8-2}-\dfrac{1}{2-\sqrt 6}$

$=\dfrac{\sqrt 3(2-\sqrt 2)}{\sqrt 2(2-\sqrt 2)}-\dfrac{1}{2-\sqrt 6}$

$=\dfrac{\sqrt 3}{\sqrt 2}-\dfrac{2+\sqrt 6}{4-6}$

$=\dfrac{\sqrt 6}{2}+\dfrac{2+\sqrt 6}{2}$

$=\dfrac{2\sqrt 6+2}{2}$

$=\sqrt 6+1$

d) $4\left(\sqrt{5-\sqrt {21}}-\sqrt{6-\sqrt{27}}-\sqrt{\dfrac{7}{2}}\right)^2$

$=2.\left(\sqrt 2.\sqrt{5-\sqrt{21}}-\sqrt 2.\sqrt{6-\sqrt{27}}-\sqrt2.\sqrt{\dfrac{7}{2}}\right)^2$

$=2.\left(\sqrt{10-2\sqrt{21}}-\sqrt{12-2\sqrt{27}}-\sqrt 7\right)^2$

$=2.\left(\sqrt{(\sqrt 7-\sqrt 3)^2}-\sqrt{(3-\sqrt 3)^2}-\sqrt 7\right)^2$

$=2.(\sqrt 7-\sqrt 3-3+\sqrt 3-\sqrt 7)^2$

$=2.(-3)^2=18$.

Đáp án:

Giải thích các bước giải:

 `a) 3 sqrt { 12 } + sqrt { 7,5 } . sqrt { 10 } - 3 sqrt { 100/3 }`

`= 3 sqrt { 4 . 3 } + sqrt { 7,5 . 10 } - 3 sqrt { 100 }/sqrt { 3 }`

`= 6 sqrt { 3 } + sqrt { 75 } - 10 sqrt { 3 }`

`= 6 sqrt { 3 } + sqrt { 25 . 3 } - 10 sqrt { 3 }`

`= 6 sqrt { 3 } + 5 sqrt { 3 } - 10 sqrt { 3 }`

`= sqrt { 3 }`

`b) sqrt { ( sqrt {6} - 2 )^2 } + sqrt { 15 - 6 sqrt {6} }`

`= | sqrt {6} - 2 | + sqrt { 9 - 6 sqrt {6} + 6 }`

`= ( sqrt {6} - 2 ) + sqrt { ( 3 - sqrt {6} )^2 }`

`= ( sqrt {6} - 2 ) + | 3 - sqrt {6} |`

`= ( sqrt {6} - 2 ) + ( 3 - sqrt {6} )`

`= sqrt {6} - 2 + 3 - sqrt {6}`

`= 1`

`c) ( 2 sqrt {3} - sqrt {6} )/( sqrt {8} - 2 ) - 1/( 2 - sqrt {6} )`

`= ( sqrt {12} - sqrt {6} )/( sqrt {8} - sqrt {4} ) - ( 2 + sqrt {6} )/(( 2 - sqrt {6} ).( 2 + sqrt {6} ))`

`= (sqrt {6} . ( sqrt {2} - 1 ))/(sqrt {4} . ( sqrt {2} - 1 )) - ( 2 + sqrt {6} )/( 4 - 6 )`

`=  sqrt {3}/sqrt {2} - ( 2 + sqrt {6} )/-2`

`= sqrt {6}/2 + ( 2 + sqrt {6} )/2`

`= ( sqrt {6} + 2 + sqrt {6} )/2`

`= ( 2 + 2 sqrt {6} )/2`

`= 1 + sqrt {6}`

`d) 4 . ( sqrt { 5 - sqrt { 21 } } - sqrt { 6 - sqrt { 27 } } - sqrt { 7/2 } )^2`

`= 2^2 . ( sqrt { 5 - sqrt { 21 } } - sqrt { 6 - sqrt { 27 } } - sqrt { 7/2 } )^2`

`= [ 2 . ( sqrt { 5 - sqrt { 21 } } - sqrt { 6 - sqrt { 27 } } - sqrt { 7/2 } )]^2`

`= [ sqrt {2} . sqrt {2} . ( sqrt { 5 - sqrt { 21 } } - sqrt { 6 - sqrt { 27 } } - sqrt { 7/2 } )]^2`

`= [ sqrt {2} . ( sqrt {2} . sqrt { 5 - sqrt { 21 } } - sqrt {2} . sqrt { 6 - sqrt { 27 } } - sqrt {2} . sqrt { 7/2 } )]^2`

`= [ sqrt {2} . ( sqrt { 10 - sqrt 2 . { 21 } } - sqrt { 12 - sqrt 2 . { 27 } } - sqrt { 7 } )]^2`

`= [ sqrt {2} . ( sqrt { 7 - sqrt 2 . { 21 } + 3 } - sqrt { 9 - sqrt 2 . { 27 } + 3 } - sqrt { 7 } )]^2`

`= [ sqrt {2} . ( sqrt { ( sqrt {7} - sqrt {3} )^2 } - sqrt { ( sqrt {9} - sqrt {3} )^2 } - sqrt { 7 } )]^2`

`= [ sqrt {2} . ( | sqrt {7} - sqrt {3} | - | 3 - sqrt {3} | - sqrt { 7 } )]^2`

`= [ sqrt {2} . ( sqrt {7} - sqrt {3} - 3 + sqrt {3} - sqrt { 7 } )]^2`

`= [ sqrt {2} . ( - 3 )]^2`

`= 2 . 9`

`= 18`