Bài 1: Tính giá trị của biểu thức:
1)\(H=\sqrt[3]{3+\sqrt{9+\frac{125}{7}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{7}}}\)
2)\(P=\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt{5}-\sqrt[4]{125}}}\)
Bài 2: Tính giá trị biểu thức: \(Q=\sqrt[10]{\frac{19+6\sqrt{10}}{2}}.\sqrt[5]{3\sqrt{2}-2\sqrt{5}}\)
\(K=\frac{\sqrt{\sqrt[4]{8}+\sqrt{\sqrt{2}-1}}-\sqrt{\sqrt[4]{8}-\sqrt{\sqrt{2}-1}}}{\sqrt{\sqrt[4]{8}-\sqrt{\sqrt{2}+1}}}\)
tính:\(\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}+\frac{1}{\sqrt{5}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{9}}\)
Tính :
a ) \(S=\frac{1}{\sqrt{1}\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+.....+\)\(\frac{1}{\sqrt{2017}+\sqrt{2019}}\)
b ) \(S=\frac{1}{\sqrt{2}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{6}}+....+\frac{1}{\sqrt{100}+\sqrt{102}}\)
c ) \(S=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.....+\frac{1}{\sqrt{100}+\sqrt{101}}\)
d ) \(S=\frac{1}{\sqrt{3}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{12}}+....+\frac{1}{\sqrt{2016}+\sqrt{2019}}\)
rút gọn biểu thức \(A=\frac{\sqrt{20}+2}{\sqrt{3}-1}-\frac{\sqrt{112}+4}{\sqrt{5}+1}+\sqrt{5}\left(\sqrt{7}-\sqrt{3}\right)\)
\(A=\left(\sqrt{3}+1\right)^2+\frac{5}{4}\sqrt{48}-\frac{2}{\sqrt{3+1}}\)
\(B=\frac{4}{3-\sqrt{5}}-\frac{3}{\sqrt{5}+\sqrt{2}}-\frac{1}{\sqrt{2}-1}\)
\(C=\sqrt{4-2\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)
Rút gọn
Giúp mình với mình cần gấp
Rút gọn biểu thức
A = \(\frac{\sqrt{3}+\sqrt{11+6\sqrt{2}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)
B = \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
C = \(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
D = \(\sqrt{28+6\sqrt{3}}-\sqrt{28-6\sqrt{3}}\)
E = \(6x+\sqrt{9x^2-12x+4}\)
F = \(5x-\sqrt{x^2+4x+4}\)
Tính P = \(\frac{4+\sqrt{3}}{\sqrt{1}+\sqrt{3}}+\frac{8+\sqrt{15}}{\sqrt{3}+\sqrt{5}}+...+\frac{2n+\sqrt{n^2-1}}{\sqrt{n-1}+\sqrt{n+1}}+...+\frac{240+\sqrt{14399}}{\sqrt{119}+\sqrt{121}}\)
Tính \(C=\sqrt{x}+\frac{\sqrt[3]{2-\sqrt{3}}.\sqrt[6]{7+4\sqrt{3}}-x}{\sqrt[4]{9-4\sqrt{5}}.\sqrt{2+\sqrt{5}}+\sqrt{x}}\)
\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{2}=\sqrt{\frac{2\left(4-\sqrt{7}\right)}{2}}-\sqrt{\frac{2\left(4+\sqrt{7}\right)}{2}}+\sqrt{2}\)
=\(\sqrt{\frac{8-2\sqrt{7}}{2}}-\sqrt{\frac{8+2\sqrt{7}}{2}}+\sqrt{2}\)
=\(\sqrt{\frac{\left(\sqrt{7}-1\right)^2}{2}}-\sqrt{\frac{\left(\sqrt{7}+1\right)^2}{2}}+\sqrt{2}\)
=\(\frac{\sqrt{7}-1}{\sqrt{2}}-\frac{\sqrt{7}+1}{\sqrt{2}}+\sqrt{2}\)
=\(\frac{-2}{\sqrt{2}}+\sqrt{2}\)
=\(-\sqrt{2}+\sqrt{2}\)
=0
Giải phương trình bậc nhất 1 ẩn sau đây:
\(\frac{2+\sqrt{3}}{3-\sqrt{5}}x-\frac{1-\sqrt{6}}{3+\sqrt{2}}\left(x-\frac{3-\sqrt{7}}{4-\sqrt{3}}\right)=\frac{15-\sqrt{11}}{2\sqrt{3}-5}\)
