Đưa biểu thức trong căn về dạng hình phương của một tổng hoặc một hiệu:
f/ \(\sqrt{8-2\sqrt{15}+}\sqrt{4-2\sqrt{3}}\)
g/ \(\sqrt{42-10\sqrt{17}+\sqrt{33-8\sqrt{17}}}\)
h/ \(\sqrt{12-2\sqrt{35}}+\sqrt{7-2\sqrt{10}}-\sqrt{49}\)
i/ \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-\sqrt{3-\sqrt{5}}\)
l/ \(\sqrt{11+4\sqrt{6}}-\sqrt{9-4\sqrt{2}}\)
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/ \(\frac{\sqrt{5}-\sqrt{15}}{1-\sqrt{3}}-\sqrt{21+4\sqrt{5}}\)
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=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10-2\sqrt{5}}}\)
Bài 1: Rút gọn biểu thức
a) \(A=\sqrt{26+15\sqrt{3}}\)
b) \(B=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)
c) \(C=\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)
d) \(D=\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\sqrt{5-\sqrt{24}}\)
e) \(E=\left(\sqrt{10}-\sqrt{2}\right)\left(\sqrt{3+\sqrt{5}}\right)\)
f) \(F=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
g) \(G=\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
h) \(H=\frac{\left(2+\sqrt{3}\right)\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\)
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=\(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
Tính: \(N=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
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)\(\sqrt{53-20\sqrt{7}}-\sqrt{64+6\sqrt{7}}\)
a. P=\(\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{6}-\sqrt{2}}+\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
b.P= (\(\frac{2}{\sqrt{3}-1}-\frac{52}{3\sqrt{3}-1}+\frac{12}{3-\sqrt{3}}\)) ( 5+\(\sqrt{27}\))
c. P= (\(\frac{2+\sqrt{2}}{\sqrt{2}+1}+1\))(\(\frac{2-\sqrt{2}}{\sqrt{2}-1}-1\))
d. P=\(\sqrt{9+\sqrt{17}}-\sqrt{9-\sqrt{17}}-\sqrt{2}\)
đ. P=(2+\(\sqrt{4+\sqrt{6+2\sqrt{5}}}\) )(\(\sqrt{10}-\sqrt{2}\) )
e. P= \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
ê. P= \(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
g. G= \(\frac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
h. H=\(\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}-\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}\)
i. I= \(\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}\)
rút gọn các biểu thức sau
a) \(\frac{4}{\sqrt{10}}\left(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\right)\)
b)\(\left(4+\sqrt{\text{15}}\right).\left(\sqrt{10}-\sqrt{6}\right).\sqrt{\text{4}-\sqrt{15}}\)
c)\(\sqrt{\text{4 }\sqrt{\text{6}}\text{ }+8\sqrt{\text{3 }}+4\sqrt{2}+18}\)
Trục căn ở mẫu:
\(a)\frac{5}{\sqrt{10}}\\ b)\frac{-2}{1-\sqrt{5}}\\ c)\frac{4}{\sqrt{3}+\sqrt{2}}\\ d)\frac{1}{3-2\sqrt{2}}\\ e)\frac{6-\sqrt{6}}{1-\sqrt{6}}\\ g)\frac{3\sqrt{2}-2\sqrt{3}}{2\left(\sqrt{3}-\sqrt{2}\right)}\\ h)\frac{\sqrt{3}-3}{\sqrt{3}-1}\\ i)\frac{\sqrt{15}}{5\sqrt{3}+3\sqrt{5}}\)