a) √(√3 - 3)2 + √4 - 2√3
b)\(\dfrac{1}{\sqrt{5}-2}\)+ \(\dfrac{\sqrt{10}-\sqrt{5}}{1-\sqrt{2}}\)
giải giúp mk 2 câu này vớiiiii ạ
1.)\(\sqrt{\left(\sqrt{3}-3\right)^2}\)+\(\sqrt{4-2\sqrt{3}}\)
2)\(\dfrac{1}{\sqrt{5}-2}\) +\(\dfrac{\sqrt{10}-\sqrt{5}}{1-\sqrt{2}}\)
3)\(\dfrac{\sqrt{2}}{\sqrt{3}-1}\) -\(\sqrt{\dfrac{3}{2}}\)
giải chi tiết giúp mk vớiiiii ạ
1)\(=\left|\sqrt{3}-3\right|+\sqrt{\left(\sqrt{3}-1\right)^2}=3-\sqrt{3}+\left|\sqrt{3}-1\right|=3-\sqrt{3}+\sqrt{3}-1=2\)
2: \(=\sqrt{5}+2-\sqrt{5}=2\)
M= \(\dfrac{3}{2}\sqrt{32x}-\dfrac{1}{3}\sqrt{18x}+\dfrac{2}{5}\sqrt{50x}-4\sqrt{2x}\) (x lớn hơn hoặc bằng 0)
giải chi tiết giúp mk vớiiiii ạ
\(M=\dfrac{3}{2}\cdot4\sqrt{2x}-\dfrac{1}{3}\cdot3\sqrt{2x}+\dfrac{2}{5}\cdot5\sqrt{2x}-4\sqrt{2x}=6\sqrt{2x}-\sqrt{2x}+2\sqrt{2x}-4\sqrt{2x}=3\sqrt{2x}\)
Câu1:\(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\)- \(\dfrac{\sqrt{6}-3}{\sqrt{2}-\sqrt{3}}\)
Câu2:\(\dfrac{\sqrt{2}}{\sqrt{3}-1}-\sqrt{\dfrac{3}{2}}\)
giải cụ thể giúp mk vớiiiii ạ
Câu 1:
\(=\sqrt{3}-\sqrt{2}-\sqrt{2}=3-2\sqrt{2}\)
1) thực hiện phép tính
d)\(\dfrac{4}{\sqrt{7}-\sqrt{3}}+\dfrac{6}{3+\sqrt{3}}+\dfrac{\sqrt{7}-7}{\sqrt{7}-1}\)
e) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
giúp mk vs ạ mk cần gấp
\(\dfrac{\sqrt{5}}{\sqrt{5}+3}+\dfrac{2\sqrt{5}}{\sqrt{5}-3}-2:\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{10}+1}\)
M.N GIÚP MK RÚT GỌN VS Ạ
\(=\dfrac{5-3\sqrt{5}+10+6\sqrt{5}}{\left(\sqrt{5}-3\right)\left(\sqrt{5}+3\right)}-\dfrac{2\sqrt{10}+2}{\sqrt{3}-\sqrt{2}}\\ =\dfrac{15+3\sqrt{5}}{5-9}-\left(2\sqrt{10}+2\right)\left(\sqrt{3}+\sqrt{2}\right)\\ =-2\sqrt{30}-4\sqrt{5}-2\sqrt{3}-2\sqrt{2}-\dfrac{15+3\sqrt{5}}{4}\\ =\dfrac{-8\sqrt{30}-16\sqrt{5}-8\sqrt{3}-8\sqrt{2}-15-3\sqrt{5}}{4}\\ =\dfrac{-8\sqrt{30}-19\sqrt{5}-8\sqrt{3}-8\sqrt{2}-15}{4}\)
\(\sqrt{\left(3-2\sqrt{5}\right)}^2+\sqrt{\left(5-2\sqrt{5}\right)^2}\)
\(\dfrac{2}{\sqrt{3}+1}-\dfrac{2}{\sqrt{3}-1}\)
\(\sqrt{7+2}\sqrt{10}-\sqrt{7-2\sqrt{10}}\)
giúp mk với ạ
1) \(=2\sqrt{5}-3+5-2\sqrt{5}=2\)
2) \(=\dfrac{2\sqrt{3}-2-2\sqrt{3}-2}{3-1}=\dfrac{-4}{2}=-2\)
3) \(=\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}=\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}=2\sqrt{2}\)
Giải 5 câu sau:
1. \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\)
2. \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}\)
3. \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{5}}\)
4. \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}\)
5. \(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}\)
1) \(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}=9+4\sqrt{5}\)
2) \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{2}-\sqrt{5}}=\dfrac{\sqrt{10}\left(\sqrt{5}-\sqrt{2}\right)}{-\left(\sqrt{5}-\sqrt{2}\right)}=-\sqrt{10}\)
3) \(\dfrac{\sqrt{20}-3\sqrt{10}}{3-\sqrt{5}}=\dfrac{\sqrt{10}\left(\sqrt{5}-3\right)}{-\left(\sqrt{5}-3\right)}=-\sqrt{10}\)
4) \(\dfrac{6-2\sqrt{5}}{3+\sqrt{5}}=\dfrac{\left(6-2\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}=\dfrac{18-6\sqrt{5}-6\sqrt{5}+10}{4}=\dfrac{28-12\sqrt{5}}{4}=7-3\sqrt{5}\)
5)\(\dfrac{9+4\sqrt{5}}{\sqrt{5}+2}=\sqrt{5}+2\)
1) rút gọn
A= \(3\sqrt{2}+5\sqrt{8}-2\sqrt{50}\)
B= \(\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{3-\sqrt{5}}\)
C= \(\sqrt{7-4\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)
Giúp mk vs ạ mk cần gấp
\(A=3\sqrt{2}+5\sqrt{8}-2\sqrt{50}\)
\(=3\sqrt{2}+10\sqrt{2}-10\sqrt{2}\)
\(=3\sqrt{2}\)
\(B=\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{3-\sqrt{5}}\)
\(=\dfrac{3-\sqrt{5}}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}+\dfrac{3+\sqrt{5}}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}\)
\(=\dfrac{3-\sqrt{5}+3+\sqrt{5}}{9-5}\)
\(=\dfrac{3}{2}\)
\(A=3\sqrt{2}+5\sqrt{8}-2\sqrt{50}\)
\(A=3\sqrt{2}+10\sqrt{2}-10\sqrt{2}=3\sqrt{2}\)
\(B=\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{3-\sqrt{5}}\)
\(B=\dfrac{3-\sqrt{5}+3+\sqrt{5}}{9-5}=\dfrac{6}{4}=\dfrac{3}{2}\)
\(C=\sqrt{7-4\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)
\(C=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(3+\sqrt{3}\right)^2}\)
\(C=2-\sqrt{3}+3+\sqrt{3}=5\)
\(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
giải giúp mình câu này với
\(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\) = \(\dfrac{2\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{-\dfrac{4}{1+\sqrt{5}}}\) = \(2\sqrt{5}-2\left(1+\sqrt{5}\right)\) = -2.