a: \(\dfrac{5+2\sqrt{5}}{\sqrt{5}+\sqrt{2}}=\dfrac{\left(5+2\sqrt{5}\right)\left(\sqrt{5}-\sqrt{2}\right)}{3}=\dfrac{5\sqrt{5}-5\sqrt{2}+10-2\sqrt{10}}{3}\)

b: \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}=\sqrt{\left(2-\sqrt{3}\right)^2}=2-\sqrt{3}\)

viết đề như vậy sao đọc được ?

có ai đọc được ko ???????????

\(\frac{1}{n\sqrt{n-1}+\left(n-1\right)\sqrt{n}}\)

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

\(=\frac{\sqrt{n-1}-\sqrt{n}}{\sqrt{n-1}\sqrt{n}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n-1}}\)

Sau đó bạn tự áp dụng vào nhé!

a: \(\left(2\sqrt6-4\sqrt3+5\sqrt2-\frac14\cdot\sqrt8\right)\cdot3\sqrt6\)

\(=\left(2\sqrt6-4\sqrt3+5\sqrt2-\frac12\sqrt2\right)\cdot3\sqrt6\)

\(=\left(2\sqrt6-4\sqrt3+\frac92\cdot\sqrt2\right)\cdot3\sqrt6\)

\(=2\sqrt6\cdot3\sqrt6-4\sqrt3\cdot3\sqrt6+\frac92\cdot\sqrt2\cdot3\sqrt6\)

\(=36-12\sqrt{18}+\frac{27}{2}\sqrt{12}=36-36\sqrt2+27\sqrt3\)

b: \(\left(\sqrt{\frac17}-\sqrt{\frac{16}{7}}+\sqrt7\right):\sqrt7=\left(\frac{\sqrt7}{7}-\frac{4\sqrt7}{7}+\sqrt7\right):\sqrt7\)

\(=\frac17-\frac47+1=\frac87-\frac47=\frac47\)

c: \(\left(\sqrt{3-\sqrt5}+\sqrt{3+\sqrt5}\right)^2\)

\(=3-\sqrt5+3+\sqrt5+2\cdot\sqrt{\left(3-\sqrt5\right)\left(3+\sqrt5\right)}\)

\(=6+2\cdot\sqrt{9-5}=6+2\cdot2=10\)