Question

giúp mình vs ạ !

Answer 1

a) \(\sqrt{125}-2\sqrt{20}-3\sqrt{80}+4\sqrt{45}=\sqrt{25.5}-2\sqrt{4.5}-3\sqrt{16.5}+4\sqrt{9.5}\)

\(=5\sqrt{5}-4\sqrt{5}-12\sqrt{5}+12\sqrt{5}=\sqrt{5}\)

b) \(10\sqrt{28}-2\sqrt{275}-3\sqrt{343}-\dfrac{3}{2}\sqrt{396}\)

\(=10\sqrt{4.7}-2\sqrt{25.11}-3\sqrt{49.7}-\dfrac{3}{2}\sqrt{36.11}\)

\(=20\sqrt{7}-10\sqrt{11}-21\sqrt{7}-9\sqrt{11}=-\sqrt{7}-19\sqrt{11}\)

c) \(\dfrac{1}{7+4\sqrt{3}}+\dfrac{1}{7-4\sqrt{3}}=\dfrac{7-4\sqrt{3}+7+4\sqrt{3}}{\left(7-4\sqrt{3}\right)\left(7+4\sqrt{3}\right)}=\dfrac{14}{1}=14\)

d) \(\dfrac{1}{2\sqrt{11}-3\sqrt{7}}=\dfrac{2\sqrt{11}+3\sqrt{7}}{\left(2\sqrt{11}-3\sqrt{7}\right)\left(2\sqrt{11}+3\sqrt{7}\right)}=\dfrac{2\sqrt{11}+3\sqrt{7}}{-19}\)

\(=-\dfrac{2\sqrt{11}+3\sqrt{7}}{19}\)

 

Answer 2

\(\sqrt{125}-2\sqrt{20}-3\sqrt{80}+4\sqrt{45}=\sqrt{5^2.5}-2.\sqrt{2^2.5}-3\sqrt{4^2.5}+4\sqrt{3^2.5}\)

\(=5\sqrt{5}-4\sqrt{5}-12\sqrt{5}+12\sqrt{5}=\sqrt{5}\)

b.

\(=10\sqrt{2^2.7}-2\sqrt{5^2.11}-3\sqrt{7^2.7}-\dfrac{3}{2}\sqrt{6^2.11}\)

\(=20\sqrt{7}-10\sqrt{11}-21\sqrt{7}-9\sqrt{11}=-\sqrt{7}-19\sqrt{11}\)

c.

\(=\dfrac{7-4\sqrt{3}}{\left(7-4\sqrt{3}\right)\left(7+4\sqrt{3}\right)}+\dfrac{7+4\sqrt{3}}{\left(7-4\sqrt{3}\right)\left(7+4\sqrt{3}\right)}=\dfrac{7-4\sqrt{3}}{49-16.3}+\dfrac{7+4\sqrt{3}}{49-16.3}\)

\(=7-4\sqrt{3}+7+4\sqrt{3}=14\)

d.

\(\dfrac{1}{2\sqrt{11}-3\sqrt{7}}=\dfrac{2\sqrt{11}+3\sqrt{7}}{\left(2\sqrt{11}+3\sqrt{7}\right)\left(2\sqrt{11}-3\sqrt{7}\right)}=\dfrac{2\sqrt{11}+3\sqrt{7}}{4.11-9.7}\)

\(=-\dfrac{2\sqrt{11}+3\sqrt{7}}{19}\)

Answer 3

a) Ta có: \(\sqrt{125}-2\sqrt{20}-3\sqrt{80}+4\sqrt{45}\)

\(=5\sqrt{5}-4\sqrt{5}-12\sqrt{5}+12\sqrt{5}\)

\(=\sqrt{5}\)

b) Ta có: \(10\sqrt{28}-2\sqrt{275}-3\sqrt{343}-\dfrac{3}{2}\sqrt{396}\)

\(=20\sqrt{7}-10\sqrt{11}-21\sqrt{7}-9\sqrt{11}\)

\(=-\sqrt{7}-19\sqrt{11}\)