\(A=\sqrt[3]{3\sqrt{21}+8}-\sqrt[3]{3\sqrt{21}-8}\)
\(\Leftrightarrow A^3=3\sqrt{21}+8-3\sqrt{21}+8+3\cdot A\cdot\sqrt[3]{\left(3\sqrt{21}\right)^2-8^2}\)
\(\Leftrightarrow A^3=16+15A\)
\(\Leftrightarrow A^3-15A-16=0\)
hay \(A\simeq4.32\)
Rút gọn biểu thức:
a) \(\sqrt{8+4\sqrt{3}}-\sqrt{8-4\sqrt{3}}\)
b) \(\dfrac{\sqrt{21+8\sqrt{5}}}{4+\sqrt{5}}.\sqrt{9-4\sqrt{5}}\)
Chứng minh đẳng thức :
a) \(A=\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}=\sqrt{2}\)
b) \(B=\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}=8\)
Giải phương trình:
a. \(3\sqrt{8x}-\sqrt{32x}+\sqrt{50x}=21\)
b. \(\sqrt{25x+50}+3\sqrt{4x+8}-2\sqrt{16x+32}=15\)
c. \(\sqrt{\left(x-2\right)^2}=12\)
d. \(\sqrt{x^2-6x+9}-3=5\)
e.\(\sqrt{\left(2x-1\right)^2}-x=3\)
f. \(\sqrt{3x-6}-x=-2\)
h. \(\sqrt{3-2x}-2=x\)
\(\sqrt[3]{27+6\sqrt{21}}+\sqrt[3]{27-6\sqrt{21}}\)
Bài: Tính giá trị các biểu thức sau
a. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
b. \(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
cho x=\(\left(\sqrt{5}-1\right)\sqrt[3]{8\sqrt{5}+16}-\sqrt{21+8\sqrt{5}}\)
tính M=\(\frac{x^4-2x^2-15}{x^{2014}}\)
Tính: \(21\sqrt{\frac{3}{7}}-\frac{13}{2\sqrt{3}-5}-\sqrt{21-12\sqrt{3}}\)
Rút gọn: \(\left(\sqrt{21}+3\right)\sqrt{5-\sqrt{21}}-\sqrt{24}\)
rút gon bieu thức
\(\left(3\sqrt{2}+\sqrt{6}\right).\sqrt{6-3\sqrt{3}}\)
\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
\(\sqrt{\dfrac{13}{4}+\sqrt{3}}-\sqrt{\dfrac{7}{4}-\sqrt{3}}\)
\(\sqrt{\dfrac{289+4\sqrt{72}}{16}}+\sqrt{\dfrac{129}{16}+\sqrt{2}}\)
\(\sqrt{11+6\sqrt{2}}-\sqrt{\sqrt{8}+3}\)
\(\sqrt{16-6\sqrt{7}}+\sqrt{10-2\sqrt{21}}\)
