a) \({\left( {\sqrt {4,1} } \right)^2} - {\left( { - \sqrt {6,1} } \right)^2}\);
b) \({\left( {\sqrt {101} } \right)^2} - \sqrt {{{\left( { - 99} \right)}^2}} \);
c) \(\sqrt {{{\left( {\sqrt 3 + 2\sqrt 2 } \right)}^2}} - \left( { - \sqrt 3 + 2\sqrt 2 } \right)\);
d) \(\sqrt {{{\left( {\sqrt {10} + 3} \right)}^2}} - \sqrt {{{\left( {\sqrt {10} - 3} \right)}^2}} \).
+ \(\sqrt {{A^2}} = \left| A \right|\) với mọi biểu thức A.
+ \({\left( {\sqrt x } \right)^2} = x\left( {x \ge 0} \right)\).
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a) \({\left( {\sqrt {4,1} } \right)^2} - {\left( { - \sqrt {6,1} } \right)^2} = 4,1 - 6,1 = - 2\);
b) \({\left( {\sqrt {101} } \right)^2} - \sqrt {{{\left( { - 99} \right)}^2}} = 101 - 99 = 2\);
c) \(\sqrt {{{\left( {\sqrt 3 + 2\sqrt 2 } \right)}^2}} - \left( { - \sqrt 3 + 2\sqrt 2 } \right) \)
\(= \left| {\sqrt 3 + 2\sqrt 2 } \right| + \sqrt 3 - 2\sqrt 2 \)
\(= \sqrt 3 + 2\sqrt 2 + \sqrt 3 - 2\sqrt 2 \)
\(= \left( {\sqrt 3 + \sqrt 3 } \right) + \left( {2\sqrt 2 - 2\sqrt 2 } \right) = 2\sqrt 3 \)
d) \(\sqrt {{{\left( {\sqrt {10} + 3} \right)}^2}} - \sqrt {{{\left( {\sqrt {10} - 3} \right)}^2}} \)
\(= \left| {\sqrt {10} + 3} \right| - \left| {\sqrt {10} - 3} \right| \)
\(= \sqrt {10} + 3 - \sqrt {10} + 3 = 6\).