mn ơi giải giúp mik bài não cũng đc a

mình cảm ơn mn nhiều ạ =))

bài 1:

a) \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}{\sqrt{2}.\sqrt{2}}=\dfrac{\sqrt{10}-\sqrt{6}}{2}\)

b) \(\dfrac{26}{5-2\sqrt{3}}=\dfrac{26\left(5+2\sqrt{3}\right)}{13}=\dfrac{130+52\sqrt{3}}{13}\)

c)\(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}=\dfrac{\left(9-2\sqrt{3}\right)\left(3\sqrt{6}-2\sqrt{2}\right)}{46}=\dfrac{27\sqrt{6}-18\sqrt{2}-18\sqrt{2}+4\sqrt{6}}{46}=\dfrac{31\sqrt{6}-36\sqrt{2}}{46}\)

Đề không khó, mỗi tội dài

Bài 2:

a: \(=3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}=14\sqrt{2x}\)

b: \(=6-4\sqrt{3}+4\sqrt{3}-8=-2\)

c: \(=\sqrt{2}+1+2-\sqrt{2}=3\)

d: \(=\dfrac{1}{\sqrt{2}}\left(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\right)+\sqrt{6}\)

\(=\dfrac{1}{\sqrt{2}}\left(\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}\right)+\sqrt{6}\)

=0

e: \(=\left(\sqrt{5}-1-2\right)\left(\sqrt{5}-1+4\right)\)

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

=5-9

=-4

f: \(=\dfrac{1}{5}\cdot5\sqrt{2}-2\cdot4\sqrt{6}-\sqrt{2}+2\sqrt{6}\)

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

a: \(=\sqrt{5}+2+\sqrt{3}+1-\sqrt{5}-\sqrt{3}=3\)

b: \(=\left(-\sqrt{5}-2+\sqrt{5}-\sqrt{3}\right)\cdot\left(2\sqrt{3}+3\right)\)

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

\(=-\sqrt{3}\left(7+4\sqrt{3}\right)=-7\sqrt{3}-12\)

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

b: \(=\dfrac{\sqrt{5}+1}{\sqrt{5}-1}+\dfrac{\sqrt{5}-1}{\sqrt{5}+1}\)

\(=\dfrac{6+2\sqrt{5}+6-2\sqrt{5}}{4}=\dfrac{12}{4}=3\)

c: \(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)

\(=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\)

e: \(=\dfrac{2\sqrt{3+\sqrt{5-2\sqrt{3}-1}}}{\sqrt{6}-\sqrt{2}}\)

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

\(=\dfrac{4-2\sqrt{3}}{2}=2-\sqrt{3}\)

a) \(\dfrac{\sqrt{2}}{\sqrt{3}}+2.\dfrac{\sqrt{3}}{\sqrt{2}}-\sqrt{6}=\dfrac{\sqrt{2}}{\sqrt{3}}+\dfrac{\sqrt{2}.\sqrt{2}.\sqrt{3}}{\sqrt{2}}-\sqrt{6}=\dfrac{\sqrt{2}}{\sqrt{3}}+\sqrt{6}-\sqrt{6}=\dfrac{\sqrt{2}}{\sqrt{3}}\)

b)

\(3\dfrac{\sqrt{2}}{\sqrt{5}}+\dfrac{\sqrt{5}}{\sqrt{2}}-2\sqrt{10}=3\dfrac{\sqrt{2}.\sqrt{5}}{5}+\dfrac{\sqrt{5}.\sqrt{2}}{2}-2\sqrt{10}\)\(=\sqrt{10}.\left[\dfrac{3}{5}+\dfrac{1}{2}-2\right]=\sqrt{10}.\left(-\dfrac{9}{10}\right)=\dfrac{-9\sqrt{10}}{10}\)

c)

\(\dfrac{-\sqrt{3}}{\sqrt{5}}+3.\dfrac{\sqrt{5}}{\sqrt{3}}-4\sqrt{15}=\dfrac{-\sqrt{15}}{5}+3.\dfrac{\sqrt{15}}{3}-4\sqrt{15}=\sqrt{15}.\left(\dfrac{-1}{5}+1-4\right)=\sqrt{15}.\left(-\dfrac{16}{5}\right)=\dfrac{-16\sqrt{15}}{5}\)

d)\(\dfrac{2\left(\sqrt{6}+2\right)}{\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}+\dfrac{2\left(\sqrt{6}-2\right)}{\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}+\dfrac{5\sqrt{6}}{6}\)

\(=\dfrac{2\left[\left(\sqrt{6}+2\right)+\left(\sqrt{6}-2\right)\right]}{6-4}+\dfrac{5\sqrt{6}}{6}=\left(2\sqrt{6}\right)+\dfrac{5\sqrt{6}}{6}=\dfrac{17\sqrt{6}}{6}\)

Kiểm tra lại nhé ^^

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

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

1: \(=2\sqrt{7}-12\sqrt{7}+15\sqrt{7}+27\sqrt{7}=32\sqrt{7}\)

3: \(=\sqrt{5}-2-\sqrt{14+6\sqrt{5}}\)

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

4: \(=2\sqrt{3}+3+4-2\sqrt{3}=7\)

5: \(=3-\sqrt{2}+3+\sqrt{2}+4-3=7\)

6: \(=\sqrt{\dfrac{6+2\sqrt{5}}{4}}+\sqrt{\dfrac{14-6\sqrt{5}}{4}}\)

\(=\dfrac{\sqrt{5}+1+3-\sqrt{5}}{2}=\dfrac{4}{2}=2\)

8: \(=\sqrt{5}-1+\sqrt{\dfrac{\left(3-\sqrt{5}\right)^2}{4}}-\sqrt{\dfrac{\left(3+\sqrt{5}\right)^2}{4}}\)

\(=\sqrt{5}-1+\dfrac{3-\sqrt{5}}{2}-\dfrac{3+\sqrt{5}}{2}\)

\(=\dfrac{2\sqrt{5}-2+3-\sqrt{5}-3-\sqrt{5}}{2}=\dfrac{-2}{2}=-1\)

a: \(=2\cdot\dfrac{4}{3}\sqrt{3}-3\cdot\dfrac{1}{9}\sqrt{3}-6\cdot\dfrac{2}{15}\sqrt{3}\)

\(=\dfrac{8}{3}\sqrt{3}-\dfrac{1}{3}\sqrt{3}-\dfrac{4}{5}\sqrt{3}=\dfrac{23}{15}\sqrt{3}\)

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

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

c: \(=6\sqrt{3}-4\sqrt{3}+\dfrac{3}{5}\cdot5\sqrt{3}=2\sqrt{3}+3\sqrt{3}=5\sqrt{3}\)

a: \(=\dfrac{2\sqrt{7}-10-6+2\sqrt{7}}{4}+4+2\sqrt{7}-\dfrac{20}{9}+\dfrac{5}{9}\sqrt{7}\)

\(=\sqrt{7}-4+\dfrac{23}{9}\sqrt{7}+\dfrac{16}{9}\)

\(=\dfrac{32}{9}\sqrt{7}-\dfrac{20}{9}\)

b:\(=\dfrac{2\sqrt{6}+4+2\sqrt{6}-4}{2}+\dfrac{5}{6}\sqrt{6}\)

\(=2\sqrt{6}+\dfrac{5}{6}\sqrt{6}=\dfrac{17}{6}\sqrt{6}\)

c: \(=\dfrac{1}{3}\sqrt{3}+\dfrac{1}{6}\sqrt{2}+\dfrac{1}{\sqrt{3}}\cdot\sqrt{\dfrac{5-2\sqrt{6}}{12}}\)

\(=\dfrac{1}{3}\sqrt{3}+\dfrac{1}{6}\sqrt{2}+\dfrac{1}{\sqrt{3}}\cdot\dfrac{\sqrt{3}-\sqrt{2}}{2\sqrt{3}}\)

\(=\dfrac{2\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}}{6}=\dfrac{3\sqrt{3}}{6}=\dfrac{\sqrt{3}}{2}\)

a: \(=\left(2\sqrt{7}+\sqrt{7}+2\sqrt{14}\right)\cdot\sqrt{7}-\left(51+14\sqrt{2}\right)\)

\(=3\sqrt{7}\cdot\sqrt{7}+2\sqrt{14}\cdot\sqrt{7}-51-14\sqrt{2}\)

\(=21-51=-30\)

b: \(=\dfrac{\sqrt{10}}{2}+\dfrac{\sqrt{10}-\sqrt{6}}{2}=\dfrac{2\sqrt{10}-\sqrt{6}}{2}\)

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

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

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