Toán Lớp 9: (3-√2).√11+6√2
(√5+√7).√12-2√35
(√2-√9). √11+2√18
√46-6√5-√29-12√5
√7-2√10-√7+2√10
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Toán Lớp 9: (3-√2).√11+6√2
(√5+√7).√12-2√35
(√2-√9). √11+2√18
√46-6√5-√29-12√5
√7-2√10-√7+2√10
Comments ( 1 )
a)7\\
b) – 2\\
c) – 7\\
d)\sqrt 5 + 2\\
e) – 2\sqrt 2
\end{array}\)
a)\left( {3 – \sqrt 2 } \right)\sqrt {11 + 6\sqrt 2 } \\
= \left( {3 – \sqrt 2 } \right)\sqrt {9 + 2.3.\sqrt 2 + 2} \\
= \left( {3 – \sqrt 2 } \right)\sqrt {{{\left( {3 + \sqrt 2 } \right)}^2}} \\
= \left( {3 – \sqrt 2 } \right)\left( {3 + \sqrt 2 } \right)\\
= 9 – 2 = 7\\
b)\left( {\sqrt 5 + \sqrt 7 } \right)\sqrt {12 – 2.\sqrt {35} } \\
= \left( {\sqrt 5 + \sqrt 7 } \right)\sqrt {7 – 2.\sqrt 7 .\sqrt 5 + 5} \\
= \left( {\sqrt 5 + \sqrt 7 } \right)\sqrt {{{\left( {\sqrt 5 – \sqrt 7 } \right)}^2}} \\
= \left( {\sqrt 5 + \sqrt 7 } \right)\left( {\sqrt 5 – \sqrt 7 } \right)\\
= 5 – 7 = – 2\\
c)\left( {\sqrt 2 – \sqrt 9 } \right)\sqrt {11 + 2\sqrt {18} } \\
= \left( {\sqrt 2 – \sqrt 9 } \right)\sqrt {\left( {9 + 2.\sqrt 9 .\sqrt 2 + 2} \right)} \\
= \left( {\sqrt 2 – \sqrt 9 } \right)\sqrt {{{\left( {\sqrt 9 + \sqrt 2 } \right)}^2}} \\
= \left( {\sqrt 2 – \sqrt 9 } \right)\left( {\sqrt 2 + \sqrt 9 } \right)\\
= 2 – 9 = – 7\\
d)\sqrt {46 – 6\sqrt 5 } – \sqrt {29 – 12\sqrt 5 } \\
= \sqrt {45 – 2.3\sqrt 5 .1 + 1} – \sqrt {20 – 2.2\sqrt 5 .3 + 9} \\
= \sqrt {{{\left( {3\sqrt 5 – 1} \right)}^2}} – \sqrt {{{\left( {2\sqrt 5 – 3} \right)}^2}} \\
= 3\sqrt 5 – 1 – \left( {2\sqrt 5 – 3} \right)\\
= \sqrt 5 + 2\\
e)\sqrt {7 – 2\sqrt {10} } – \sqrt {7 + 2\sqrt {10} } \\
= \sqrt {5 – 2.\sqrt 5 .\sqrt 2 + 2} – \sqrt {5 + 2.\sqrt 5 .\sqrt 2 + 2} \\
= \sqrt {{{\left( {\sqrt 5 – \sqrt 2 } \right)}^2}} – \sqrt {{{\left( {\sqrt 5 + \sqrt 2 } \right)}^2}} \\
= \sqrt 5 – \sqrt 2 – \sqrt 5 – \sqrt 2 \\
= – 2\sqrt 2
\end{array}\)