\(=\sqrt{5}-\sqrt{3}+\sqrt{5}-2=2\sqrt{5}-2-\sqrt{3}\)

2 mũ 48-2 căn 15      +  3

Đặt \(N=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)

\(\Rightarrow N\sqrt{2}=\sqrt{8+2\sqrt{7}}-\sqrt{8-2\sqrt{7}}\)

\(=\sqrt{\left(\sqrt{7}+1\right)^2}-\sqrt{\left(\sqrt{7}-1\right)^2}\)

\(=\sqrt{7}+1-\sqrt{7}+1=2\)

\(\Rightarrow N=\sqrt{2}\)

\(\Rightarrow M=N-\sqrt{8}=\sqrt{2}-\sqrt{8}\)

\(A=\sqrt{5}.\left(\sqrt{20}-3\right)+\sqrt{45}.\)

\(=\sqrt{5}.\left(\sqrt{4.5}-3\right)+\sqrt{9.5}\)

\(=\sqrt{5}.\left(2\sqrt{5}-3\right)+3\sqrt{5}\)

\(=\sqrt{5}.2\sqrt{5}-3\sqrt{5}+3\sqrt{5}\)

\(=2.\sqrt{5}^2=2.5=10\)

\(3\sqrt{8}-\sqrt{50}-\sqrt{\left(\sqrt{2}-1\right)^2}\)

\(=6\sqrt{2}-5\sqrt{2}-\left(\sqrt{2}-1\right)\)

\(=\sqrt{2}-\sqrt{2}+1\)

\(=1\)

Bạn cần viết đề bằng công thức toán (biểu tượng $\sum$ bên trái khung soạn thảo) để được hỗ trợ tốt hơn.

\(\sqrt{\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}}+\sqrt{\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}}\)

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

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

\(=\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}=2\sqrt{3}\)

a: ĐKXĐ: a>=0; a<>4

b: \(M=\dfrac{a\sqrt{a}-a\sqrt{a}+2a-a-2\sqrt{a}}{a-4}=\dfrac{a-2\sqrt{a}}{a-4}=\dfrac{\sqrt{a}}{\sqrt{a}+2}\)

c: Khi a=9 thì \(M=\dfrac{3}{3+2}=\dfrac{3}{5}\)