a. \(\dfrac{\sqrt{2}.\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{7}.\left(\sqrt{3}+\sqrt{5}\right)}=\dfrac{\sqrt{2}}{\sqrt{7}}=\sqrt{\dfrac{2}{7}}\)

d. \(\dfrac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}=\dfrac{\sqrt{5-2\sqrt{5}+1}}{\sqrt{5}-1}=\dfrac{\left(\sqrt{5}-1\right)^2}{\sqrt{5}-1}=\sqrt{5}-1\)

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

d: \(D=\dfrac{2}{x^2-y^2}\cdot\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\)

\(=\dfrac{2}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{3\left(x+y\right)}{2}\)

\(=\dfrac{3}{x-y}\)

óc vật

\(A=\sqrt{27}-2\sqrt{12}-\sqrt{75}\)

\(A=\sqrt{9.3}-2\sqrt{3.4}-\sqrt{25.3}\)

\(A=3\sqrt{3}-4\sqrt{3}-5\sqrt{3}\)

\(A=-6\sqrt{3}\)

\(B=\frac{1}{3+\sqrt{7}}+\frac{1}{3-\sqrt{7}}\)

\(B=\frac{3-\sqrt{7}+3\sqrt{7}}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}\)

\(B=\frac{6}{9-7}=3\)

\(A=\sqrt{27}-2\sqrt{12}-\sqrt{75}\)

\(=\sqrt{3^2.3}-2.\sqrt{2^2.3}-\sqrt{5^2.3}\)

\(=3\sqrt{3}-4\sqrt{3}-5\sqrt{3}\)

\(=-6\sqrt{3}\)

vậy \(A=-6\sqrt{3}\)

\(B=\frac{1}{3+\sqrt{7}}+\frac{1}{3-\sqrt{7}}\)

\(B=\frac{3-\sqrt{7}}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}+\frac{3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}\)

\(B=\frac{3-\sqrt{7}+3+\sqrt{7}}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}\)

\(B=\frac{6}{9-7}\)

\(B=\frac{6}{2}\)

\(B=3\)

vậy \(B=3\)

 a) \(\frac{\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{7\left(\sqrt{3}+\sqrt{5}\right)}}=\) \(\frac{\sqrt{2}}{\sqrt{7}}\)

 b ) \(\frac{15\sqrt{2}+9\sqrt{3}}{3\sqrt{3}+3\sqrt{5}}=\frac{3\left(5\sqrt{2}+3\sqrt{3}\right)}{3\left(\sqrt{3}+\sqrt{5}\right)}\)\(=\frac{5\sqrt{2}+3\sqrt{3}}{\sqrt{3}+\sqrt{5}}\)

c)\(\frac{\sqrt{2}-\sqrt{6}+\sqrt{3}-\sqrt{9}+\sqrt{4}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\) =  \(\frac{\sqrt{2}\left(1-\sqrt{3}\right)+\sqrt{3}\left(1-\sqrt{3}\right)+\sqrt{4}\left(1-\sqrt{3}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)\(=\frac{\left(1-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1-\sqrt{3}\)

 d) \(\frac{\sqrt{\left(\sqrt{5}-1\right)^2}}{\sqrt{5}-1}=\frac{\sqrt{5}-1}{\sqrt{5}-1}=1\)

a: \(\frac{\sqrt6+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)

\(=\frac{\sqrt2\left(\sqrt3+\sqrt5\right)}{\sqrt7\left(\sqrt3+\sqrt5\right)}\)

\(=\frac{\sqrt2}{\sqrt7}=\frac{\sqrt{14}}{7}\)

b: \(\frac{\sqrt{450}+3\cdot\sqrt{27}}{3\sqrt3+\sqrt{45}}\)

\(=\frac{15\cdot\sqrt2+9\sqrt3}{3\sqrt3+3\sqrt5}=\frac{3\cdot\left(5\sqrt2+3\sqrt3\right)}{3\left(\sqrt3+\sqrt5\right)}\)

\(=\frac{5\sqrt2+3\sqrt3}{\sqrt5+\sqrt3}=\frac{\left(5\sqrt2+3\sqrt3\right)\left(\sqrt5-\sqrt3\right)}{2}=\frac{5\sqrt{10}-5\sqrt3+3\sqrt{15}-9}{2}\)

c: \(\frac{\sqrt2+\sqrt3+\sqrt4-\sqrt6-\sqrt9-\sqrt{12}}{\sqrt2+\sqrt3+\sqrt4}\)

\(=\frac{\sqrt2+\sqrt3+\sqrt4-\sqrt3\left(\sqrt2+\sqrt3+\sqrt4\right)}{\sqrt2+\sqrt3+\sqrt4}\)

\(=\frac{\left(\sqrt2+\sqrt3+\sqrt4\right)\left(1-\sqrt3\right)}{\sqrt2+\sqrt3+\sqrt4}=1-\sqrt3\)

d: \(\frac{\sqrt{6-2\sqrt5}}{\sqrt5-1}\)

\(=\frac{\sqrt{\left(\sqrt5-1\right)^2}}{\sqrt5-1}\)

\(=\frac{\sqrt5-1}{\sqrt5-1}=1\)

Rút gọn các biểu thức sau với x≥0x≥0:

a) 2\(\sqrt{3x}\)-4\(\sqrt{3x}\)+27-3\(\sqrt{3x}\)=27-5\(\sqrt{3x}\)

b)3\(\sqrt{2x}\)-5\(\sqrt{8x}\)+7\(\sqrt{18x}\)+28

=3\(\sqrt{2x}\)-10\(\sqrt{2x}\)+21\(\sqrt{2x}\)+28

=14\(\sqrt{2x}\)+28=14(\(\sqrt{2x}\)+2)

a) \(2\sqrt{3x}-4\sqrt{3x}+27-3\sqrt{3x}\)

\(=\left(2\sqrt{3x}-4\sqrt{3x}-3\sqrt{3x}\right)+27\)

\(=-5\sqrt{3x}+27\)