1) Rút gọn
a)A=\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
b)B=\(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
c)P=\(\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-2\sqrt{2}\)
2) Rút gọn
\(\sqrt{0,25\sqrt{961}+2\sqrt{10}+\sqrt{15}+\sqrt{6}}\)
3) So sánh
a)\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\) và 0
b)\(\sqrt{2002}+\sqrt{2004}\) và \(2\sqrt{2003}\)
Trục căn thức ở mẫu và rút gọn:
a) \(\frac{20}{3+\sqrt{5}+\sqrt{2+2\sqrt{5}}}\)
b) \(\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2.\sqrt{3+2\sqrt{5}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
Tính
\(a,F=\sqrt{13-\sqrt{160}}-\sqrt{53-4\sqrt{9}}\)
\(b,A=\sqrt{13-30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
\(c,D=\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-2\sqrt{2}\)
\(d,M=\sqrt{0,25\sqrt{961}+2\sqrt{10}+\sqrt{15}+\sqrt{6}}\)
rút gọn biểu thức :
A= \(\dfrac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\).
B= \(\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\).
C= \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\).
bài 1 rút gọn
a)\(\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}\)
b)\(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)
c)\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
bài 2
a) \(\frac{\sqrt{7}-\sqrt{14}}{1-\sqrt{2}}\)
b)\(\frac{\sqrt{6-5\sqrt{3}}}{2\sqrt{2}-10}\)
c) \(\frac{7-2\sqrt{10}}{5-\sqrt{10}}\)
Rút gọn các biểu thức sau:
a \(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
b \(\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\)
c \(\sqrt[3]{\sqrt{5}+2}-\sqrt[3]{\sqrt{5}-2}\)
d \(\dfrac{10}{\sqrt[3]{9}-\sqrt[3]{6}+\sqrt[3]{4}}\left(\dfrac{1+\sqrt{2}}{\sqrt{4-2\sqrt{3}}}:\dfrac{\sqrt{3}+1}{\sqrt{2}-1}\right)\)
Rút gọn
A=\(\sqrt{8-2\sqrt{15}}\)
B=\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
C=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
D=\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
bài 1:
a) Rút gọn biểu thức : \(\sqrt{\frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}:\frac{2}{\sqrt{3}-1}\)
b) giải phương trình sau: \(\sqrt{\frac{1}{4}x^2+x+1}-\sqrt{6-2\sqrt{5}}=0\)
c) tính A= \(\left(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\right)^3\)
d) rút gọn biểu thức B= \(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\)
Rút gọn các biểu thức sau:
a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\left(\sqrt{2}-3\sqrt{0,4}\right)\) b) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
c) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}\) d) \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
Rút gọn:
\(A=\sqrt{11-2\sqrt{10}}+\sqrt{9-2\sqrt{4}}-\sqrt{10}-\sqrt{7}\)
\(B=\frac{\sqrt{3}+\sqrt{11+2\sqrt{6}}-\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{6+2\sqrt{5}}-\sqrt{7+2\sqrt{10}}}\)
