Ta có :
\(B.\sqrt{2}=\left(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\right).\sqrt{2}\)
\(=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}-2\)
\(=\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{\left(\sqrt{5}-1\right)^2}-2\)
\(=\sqrt{5}+1-\left(\sqrt{5}-1\right)-2=0\)
\(\Rightarrow B=0\)
Rút gọn 1 / sqrt (2) - sqrt (3) -sqrt(3)-sqrt(5)+1/sqrt(5)-sqrt(7)
Rút gọn biểu thức sau
a)\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
b)\(\sqrt{2+\sqrt{3}}\sqrt{2+\sqrt{2+\sqrt{3}}.\sqrt{2}}-\sqrt{2+\sqrt{2}}\)
Rút gọn:
a) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+\sqrt{48}}}}\)
b) \(\dfrac{\sqrt{3}-\sqrt{5+\sqrt{24}}+\sqrt{\sqrt{72}+11}}{\sqrt{6+\sqrt{20}}+\sqrt{2}-\sqrt{7+\sqrt{40}}}\)
Rút gọn:
A= \(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\)
B= \(\sqrt[3]{20+14\sqrt{2}}-\sqrt[3]{14\sqrt{2}-20}\)
rút gọn biểu thức \(A=\frac{\sqrt{20}+2}{\sqrt{3}-1}-\frac{\sqrt{112}+4}{\sqrt{5}+1}+\sqrt{5}\left(\sqrt{7}-\sqrt{3}\right)\)
1.Rút gọn:
a) \(A=\sqrt{2+\sqrt{3}.}\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2+\sqrt{3}}}\)
b) \(B=\left(\frac{\sqrt{x}}{\sqrt{xy}-y}-\frac{\sqrt{y}}{\sqrt{xy}-x}\right).\left(x\sqrt{y}-y\sqrt{x}\right)\)
c) \(C=\sqrt{\left(3-\sqrt{5}\right)^2+\sqrt{6}-2\sqrt{5}}\)
\(A=\left(\sqrt{3}+1\right)^2+\frac{5}{4}\sqrt{48}-\frac{2}{\sqrt{3+1}}\)
\(B=\frac{4}{3-\sqrt{5}}-\frac{3}{\sqrt{5}+\sqrt{2}}-\frac{1}{\sqrt{2}-1}\)
\(C=\sqrt{4-2\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)
Rút gọn
Giúp mình với mình cần gấp
Rút gọn biểu thức sau:
\(\sqrt[3]{\sqrt{5}+2}-\sqrt[3]{\sqrt{5}-2}\)
Rút gọn
1) \(B=\sqrt{\sqrt{7}+6+\sqrt{13-2\sqrt{64-6\sqrt{7}}}}\)
2) \(C=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
3) \(D=\frac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}+\sqrt{2}}\)
