1.tính. a,√14-2√33 b,√7+2√10 c,√8-2√15 d,√14-6√5 e,√44+6√35 f,√4-√15
2.Rút gọn. F=√11-6√2-√3-√2 G=√46-6√5-29+√12√5 H=√13-√160-√53+4√90
làm giúp mk vs ạ mk cần gấp, thank you
1.tính. a,√14-2√33 b,√7+2√10 c,√8-2√15 d,√14-6√5 e,√44+6√35 f,√4-√15 2.Rút gọn. F=√11-6√2-√3-√2 G=√46-6√5-29+√12√5 H=√13-√160-√53+4√90 làm
By Harper
Đáp án:
$\begin{array}{l}
1)a)\sqrt {14 – 2\sqrt {33} } \\
= \sqrt {11 – 2.\sqrt {11} .\sqrt 3 + 3} \\
= \sqrt {{{\left( {\sqrt {11} – \sqrt 3 } \right)}^2}} \\
= \sqrt {11} – \sqrt 3 \\
b)\sqrt {7 + 2\sqrt {10} } \\
= \sqrt {5 + 2.\sqrt 5 .\sqrt 2 + 2} \\
= \sqrt {{{\left( {\sqrt 5 + \sqrt 2 } \right)}^2}} \\
= \sqrt 5 + \sqrt 2 \\
c)\sqrt {8 – 2\sqrt {15} } \\
= \sqrt {5 – 2.\sqrt 5 .\sqrt 3 + 3} \\
= \sqrt {{{\left( {\sqrt 5 – \sqrt 3 } \right)}^2}} \\
= \sqrt 5 – \sqrt 3 \\
d)\sqrt {14 – 6\sqrt 5 } \\
= \sqrt {9 – 2.3\sqrt 5 + 5} \\
= \sqrt {{{\left( {3 – \sqrt 5 } \right)}^2}} \\
= 3 – \sqrt 5 \\
e)\sqrt {44 + 6\sqrt {35} } \\
= \sqrt {35 + 2.3.\sqrt {35} + 9} \\
= \sqrt {35} + 3\\
f)\sqrt {4 – \sqrt {15} } \\
= \frac{1}{{\sqrt 2 }}.\sqrt {8 – 2\sqrt {15} } \\
= \frac{1}{{\sqrt 2 }}.\sqrt {{{\left( {\sqrt 5 – \sqrt 3 } \right)}^2}} \\
= \frac{{\sqrt 2 .\left( {\sqrt 5 – \sqrt 3 } \right)}}{2}\\
= \frac{{\sqrt {10} – \sqrt 6 }}{2}\\
2)F = \sqrt {11 – 6\sqrt 2 } – \sqrt 3 – \sqrt 2 \\
= \sqrt {9 – 2.3.\sqrt 2 + 2} – \sqrt 3 – \sqrt 2 \\
= 3 – \sqrt 2 – \sqrt 3 – \sqrt 2 \\
= 3 – \sqrt 3 – 2\sqrt 2 \\
G = \sqrt {46 – 6\sqrt 5 } – 29 + \sqrt {12\sqrt 5 } \\
= \sqrt {45 – 2.3\sqrt 5 + 1} – 29 + \sqrt {12\sqrt 5 } \\
= \sqrt {{{\left( {3\sqrt 5 – 1} \right)}^2}} – 29 + 2\sqrt {3\sqrt 5 } \\
= 3\sqrt 5 – 1 – 29 + 2\sqrt {3\sqrt 5 } \\
= 3\sqrt 5 – 30 + 2\sqrt {3\sqrt 5 }
\end{array}$