Question

[Phạm Mạnh Kiên]

có ai biết giải bài này không giúp mình với mình đang cần gấp, xin cảm ơn

Bài 20: rút gọn 

1, \(\sqrt{9-4\sqrt{5}}.\sqrt{9+4\sqrt{5}}\)

2, \(\left(2\sqrt{2}-6\right).\sqrt{11+6\sqrt{2}}\)

3, \(\sqrt{2}.\sqrt{2-\sqrt{3}}\left(\sqrt{3}+1\right)\)

4, \(\sqrt{2-\sqrt{3}}\left(\sqrt{6}-\sqrt{2}\right).\left(2+\sqrt{3}\right)\)

5, \(\sqrt{27+10\sqrt{2}}:\dfrac{1}{\sqrt{\left(\sqrt{2}-5\right)^2}}\)

Bài 21: rút gọn 

1, \(5\sqrt{\dfrac{1}{5}}\)                         2,  \(\dfrac{12}{5}\sqrt{\dfrac{5}{4}}\)

3, \(\dfrac{30}{5\sqrt{6}}\)                          4, \(\dfrac{20}{2\sqrt{5}}\)

5, \(\dfrac{2-\sqrt{2}}{\sqrt{2}}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

Bài 20:

a) \(\sqrt{9-4\sqrt{5}}\cdot\sqrt{9+4\sqrt{5}}=\sqrt{81-80}=1\)

b) \(\left(2\sqrt{2}-6\right)\cdot\sqrt{11+6\sqrt{2}}=2\left(\sqrt{2}-3\right)\left(3+\sqrt{2}\right)\)

\(=2\left(2-9\right)=2\cdot\left(-7\right)=-14\)

c: \(\sqrt{2}\cdot\sqrt{2-\sqrt{3}}\cdot\left(\sqrt{3}+1\right)\)

\(=\sqrt{4-2\sqrt{3}}\cdot\left(\sqrt{3}+1\right)\)

\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)\)

=2

d) \(\sqrt{2-\sqrt{3}}\cdot\left(\sqrt{6}-\sqrt{2}\right)\left(2+\sqrt{3}\right)\)

\(=\sqrt{4-2\sqrt{3}}\cdot\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)

\(=\left(4-2\sqrt{3}\right)\left(2+\sqrt{3}\right)\)

\(=8+4\sqrt{3}-4\sqrt{3}-6\)

=2

Answer 2

[Phạm Mạnh Kiên]

cảm ơn anh ạ