Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Rut gon:
a) \(\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\)
b) \(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
c) \(\sqrt[3]{20+14\sqrt{2}}-\sqrt[3]{14\sqrt{2}-20}\)
1/ Thực hiện phép tính rút gọn biểu thức
a/ \(\sqrt[3]{\sqrt{3}+\sqrt{2}.}\sqrt[6]{5-2\sqrt{6}}\)
b/ \(\sqrt[6]{4\sqrt{5}+9}.\sqrt[3]{2-\sqrt{5}}\)
c/ \(\dfrac{\sqrt[3]{4}+\sqrt[3]{2}+2}{\sqrt[3]{4}+\sqrt[3]{2}+1}\)
d) \(\sqrt[3]{20+14\sqrt{2}}+\sqrt{20-14\sqrt{2}}\)
giúp mình với
rút gọn biểu thức
a) frac{3}{2+sqrt{3}}+frac{13}{4-sqrt{3}}+frac{6}{sqrt{3}}
b) left(frac{sqrt{14}-sqrt{7}}{sqrt{2}-1}+frac{sqrt{15}-sqrt{5}}{sqrt{3}-1}right):frac{1}{sqrt{7}-sqrt{5}}
c) sqrt{left(2+sqrt{3}right)^2}-sqrt{28-10sqrt{3}}
d) frac{3}{3+2sqrt{3}}+frac{3}{3-2sqrt{3}}
e) sqrt{20}-15sqrt{frac{1}{5}}+sqrt{left(1-sqrt{5}right)^2}
Đọc tiếp
rút gọn biểu thức
a) \(\frac{3}{2+\sqrt{3}}+\frac{13}{4-\sqrt{3}}+\frac{6}{\sqrt{3}}\)
b) \(\left(\frac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
c) \(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
d) \(\frac{3}{3+2\sqrt{3}}+\frac{3}{3-2\sqrt{3}}\)
e) \(\sqrt{20}-15\sqrt{\frac{1}{5}}+\sqrt{\left(1-\sqrt{5}\right)^2}\)
Cho biểu thức \(P=x^3+y^3-3\left(x+y\right)+2021\). Tính giá trị biểu thức P với :
\(x=\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\)
và \(y=\sqrt[3]{3-2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\)
Tính giá trị các biểu thức sau:
a) \(A=\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
b) \(A=\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
c) \(A=\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
Bài 1: Tính
1, Aleft(1-frac{5+sqrt{5}}{1+sqrt{5}}right).left(frac{5-sqrt{5}}{1-sqrt{5}}-1right)
2, Bleft(frac{3sqrt{125}}{15}-frac{10-4sqrt{6}}{sqrt{5}-2}right).frac{1}{sqrt{5}}
3, Cleft(frac{sqrt{1000}}{100}-frac{5sqrt{2}-2sqrt{5}}{2sqrt{5}-8}right).frac{sqrt{10}}{10}
4, Dfrac{1}{sqrt{49+20sqrt{6}}}-frac{1}{sqrt{49-20sqrt{6}}}+frac{1}{sqrt{7-4sqrt{3}}}
5, Efrac{1}{sqrt{4-2sqrt{3}}}-frac{1}{sqrt{7-sqrt{48}}}+frac{3}{sqrt{14-6sqrt{5}}}
6, Ffrac{1}{sqrt{2}-sqrt{3}}sqrt{frac{3sqrt{2}-2sqrt{3}...
Đọc tiếp
Bài 1: Tính
1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)
3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)
4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)
5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)
6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)
rút gọn biểu thức a) left(sqrt{7}-sqrt{2}right).left(sqrt{9+2sqrt{14}}right)b) sqrt{sqrt{13}-sqrt{3-sqrt{13}}-4sqrt{3}}c) sqrt{80-sqrt{321-16sqrt{5}}-sqrt{226-80sqrt{5}-sqrt{89-25sqrt{5}}}}d) dfrac{1}{sqrt{8}+sqrt{7}}+sqrt{175}-dfrac{6sqrt{2}-4}{3-sqrt{2}}e) dfrac{sqrt{6-sqrt{11}}}{sqrt{22}-sqrt{2}}+dfrac{6}{sqrt{2}}-dfrac{3}{sqrt{2}+1}f) dfrac{sqrt{2}}{2sqrt{2}+sqrt{3}+sqrt{5}}+dfrac{sqrt{2}}{2sqrt{2}-sqrt{3}-sqrt{5}}g) dfrac{sqrt{2}+sqrt{3}+sqrt{6}+sqrt{8}+4}{sqrt{2}+sqrt{3}+sqrt{4}}
Đọc tiếp
rút gọn biểu thức
a) \(\left(\sqrt{7}-\sqrt{2}\right).\left(\sqrt{9+2\sqrt{14}}\right)\)
b) \(\sqrt{\sqrt{13}-\sqrt{3-\sqrt{13}}-4\sqrt{3}}\)
c) \(\sqrt{80-\sqrt{321-16\sqrt{5}}-\sqrt{226-80\sqrt{5}-\sqrt{89-25\sqrt{5}}}}\)
d) \(\dfrac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-\dfrac{6\sqrt{2}-4}{3-\sqrt{2}}\)
e) \(\dfrac{\sqrt{6-\sqrt{11}}}{\sqrt{22}-\sqrt{2}}+\dfrac{6}{\sqrt{2}}-\dfrac{3}{\sqrt{2}+1}\)
f) \(\dfrac{\sqrt{2}}{2\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{\sqrt{2}}{2\sqrt{2}-\sqrt{3}-\sqrt{5}}\)
g) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Tính:Asqrt{27}-2sqrt{48}+3sqrt{75}Bsqrt{left(sqrt{5}-2right)^2}-sqrt{left(sqrt{5}-3right)^2}Csqrt{left(2sqrt{3}+1right)^2}+sqrt{left(2sqrt{3}-5right)^2}Dsqrt{9-4sqrt{5}}-sqrt{14+6sqrt{5}}Edfrac{4}{sqrt{5}-2}-dfrac{32}{sqrt{5}+1}Mdfrac{10}{3sqrt{2}-4}+dfrac{28}{3sqrt{2}+2} please help ;-;
Đọc tiếp
Tính:
\(A=\sqrt{27}-2\sqrt{48}+3\sqrt{75}\)
\(B=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{\left(\sqrt{5}-3\right)^2}\)
\(C=\sqrt{\left(2\sqrt{3}+1\right)^2}+\sqrt{\left(2\sqrt{3}-5\right)^2}\)
\(D=\sqrt{9-4\sqrt{5}}-\sqrt{14+6\sqrt{5}}\)
\(E=\dfrac{4}{\sqrt{5}-2}-\dfrac{32}{\sqrt{5}+1}\)
\(M=\dfrac{10}{3\sqrt{2}-4}+\dfrac{28}{3\sqrt{2}+2}\)
please help ;-;
Thu gọn B= \(21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{5}\)
Thu gọn A= \(\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)