A/đặt A=\(\sqrt{30+12\sqrt{6}}+\sqrt{30-12\sqrt{6}}\)
\(\Leftrightarrow A^2=60+\sqrt{\left(30+12\sqrt{6}\right)\left(30-12\sqrt{6}\right)}\)
=\(60+6=66\)
\(\Leftrightarrow A=\sqrt{66}\)
B/ đặt B=\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
\(\Leftrightarrow B^2=8-\sqrt{\left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)}=5\)
\(\Leftrightarrow B=\sqrt{5}\)
\(\Leftrightarrow B-\sqrt{2}=\sqrt{5}-\sqrt{2}\)
hay \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\) \(-\sqrt{2}=\sqrt{5}-\sqrt{2}\)
Thực hiện phép tính:
a) \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
c)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{5}}\)
e)\(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
g)\(\sqrt{43+24\sqrt{3}}-\sqrt{49-\sqrt{8\sqrt{3}}}\)
h)\(\sqrt{53-20\sqrt{7}}-\sqrt{64+6\sqrt{7}}\)
Tính A = \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}+\left(\sqrt{3}+1\right).\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
a. P= (\(3+\sqrt{2}+\sqrt{6}\))(\(\sqrt{6-3\sqrt{3}}\))
b. A=(\(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\)): (\(\sqrt{6}+11\))
c. B= \(\frac{\sqrt{8-2\sqrt{12}}}{\sqrt{3}-1}\)-\(\sqrt{8}\)
d. C= \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)
đ. D=\(\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
e. E= \(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
ê. G= \(\sqrt{4+5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
g. H=\(\frac{2\sqrt{4+\sqrt{5+21+\sqrt{80}}}}{\sqrt{10}-\sqrt{2}}\)
i. I=\(\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}+\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}\)
k. K=\(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
Rút gọn biểu thức :
a) \(A=\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}\)
b) \(B=\frac{2+\sqrt{6}+\sqrt{10}+\sqrt{2}+\sqrt{3}+\sqrt{5}}{\sqrt{8}+\sqrt{12}+\sqrt{20}}.\frac{\sqrt{2}-1}{3}\)
Đưa biểu thức trong căn về dạng hình phương của một tổng hoặc một hiệu:
a/ \(\sqrt{7-2\sqrt{10}}-\sqrt{6-2\sqrt{5}}\)
b/ \(\sqrt{33-12\sqrt{6}}+\sqrt{15-6\sqrt{6}}\)
c/\(\sqrt{9-4\sqrt{5}}+\sqrt{12-2\sqrt{35}}\)
d/ \(\sqrt{4-2\sqrt{3}}+\sqrt{28-10\sqrt{3}}\)
e/ \(\frac{\sqrt{5}-\sqrt{15}}{1-\sqrt{3}}-\sqrt{21+4\sqrt{5}}\)
thực hiện phép tính
\(a,\sqrt{75}+\sqrt{\left(\sqrt{3}-2\right)^2}-30\sqrt{\frac{3}{25}}\)
\(b,\sqrt{11-4\sqrt{7}}-\frac{12}{1+\sqrt{7}}\)
\(\frac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{4}{1-\sqrt{7}}\)
Rút gọn
H=\(\left(\sqrt{3}-1\right)\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
F=\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
G=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
E=\(\frac{2\sqrt{3+\sqrt{5-13+\sqrt{48}}}}{\sqrt{6}+\sqrt{2}}\)
D=\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
Z=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10-2\sqrt{5}}}\)
Rút gọn biểu thức:
\(a,\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\)
\(b,\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
