Violympic toán 9
Các câu hỏi tương tự
1. Thực hiện các phép tính sau:
a. \(\sqrt{\left(2\sqrt{2}-3\right)^2}+\sqrt{11+6\sqrt{2}}\)
b. \(\sqrt{29-12\sqrt{5}}-\sqrt{29+12\sqrt{5}}\)
c. \(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)
Chứng minh các đẳng thức:
a) \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)=1
b)\(\dfrac{\left(5+2\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{\sqrt{2}+\sqrt{3}}\)-1 =0
c) \(\sqrt{26+15\sqrt{3}}+\sqrt{26-15\sqrt{3}}-5\sqrt{\dfrac{3}{2}}=\dfrac{\sqrt{6}}{2}\)
Rút gọn
B= \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}-1\)
Tính \(E=\sqrt{\left|12\sqrt{5}-29\right|}-\sqrt{12\sqrt{5}+29}\)
Cm đẳng thức
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\tan\left(45\right)\)
Tính:a. Asqrt{12}-2sqrt{48}+dfrac{7}{5}sqrt{75}b. Bsqrt{14-6sqrt{5}}+sqrt{left(2-sqrt{5}right)^2}c. Cleft(sqrt{6}-sqrt{2}right)sqrt{2+sqrt{3}}d. Ddfrac{5+sqrt{5}}{sqrt{5}+2}+dfrac{sqrt{5}-5}{sqrt{5}}-dfrac{11}{2sqrt{5}+3}
Đọc tiếp
Tính:
\(a.\) \(A=\sqrt{12}-2\sqrt{48}+\dfrac{7}{5}\sqrt{75}\)
\(b.\) \(B=\sqrt{14-6\sqrt{5}}+\sqrt{\left(2-\sqrt{5}\right)^2}\)
\(c.\) \(C=\left(\sqrt{6}-\sqrt{2}\right)\sqrt{2+\sqrt{3}}\)
\(d.\) \(D=\dfrac{5+\sqrt{5}}{\sqrt{5}+2}+\dfrac{\sqrt{5}-5}{\sqrt{5}}-\dfrac{11}{2\sqrt{5}+3}\)
Rút gọn
a, frac{2sqrt{3-1}}{sqrt{15}}-frac{2-sqrt{5}}{sqrt{3}}-frac{4sqrt{15}-10sqrt{3}}{15}
b, left(sqrt{a}-frac{1}{sqrt{a}}right)left(frac{sqrt{a}+1}{sqrt{a-1}}+frac{sqrt{a-1}}{sqrt{a}+1}right)
c, sqrt{4+sqrt{7}-sqrt{4-sqrt{7}}}
d, 6+2sqrt{2}.3-sqrt{4+sqrt{2sqrt{3}}}
e, sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}
Help me !!!
Đọc tiếp
Rút gọn
a, \(\frac{2\sqrt{3-1}}{\sqrt{15}}-\frac{2-\sqrt{5}}{\sqrt{3}}-\frac{4\sqrt{15}-10\sqrt{3}}{15}\)
b, \(\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\left(\frac{\sqrt{a}+1}{\sqrt{a-1}}+\frac{\sqrt{a-1}}{\sqrt{a}+1}\right)\)
c, \(\sqrt{4+\sqrt{7}-\sqrt{4-\sqrt{7}}}\)
d, \(6+2\sqrt{2}.3-\sqrt{4+\sqrt{2\sqrt{3}}}\)
e, \(\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
Help me !!!
Bài 1: Rút gọn biểu thức
a) Asqrt{26+15sqrt{3}}
b) Bsqrt{4+sqrt{7}}-sqrt{4-sqrt{7}}-sqrt{2}
c) Csqrt{8-2sqrt{15}}-sqrt{8+2sqrt{15}}
d) Dleft(sqrt{6}-2right)left(5+sqrt{24}right)sqrt{5-sqrt{24}}
e) Eleft(sqrt{10}-sqrt{2}right)left(sqrt{3+sqrt{5}}right)
f) Fsqrt{sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}}
g) Gleft(2-sqrt{3}right)sqrt{26+15sqrt{3}}-left(2+sqrt{3}right)sqrt{26-15sqrt{3}}
h) Hfrac{left(2+sqrt{3}right)sqrt{2-sqrt{3}}}{sqrt{2+sqrt{3}}}
Đọc tiếp
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) \(H=\frac{\left(2+\sqrt{3}\right)\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\)
Tính
\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\)
\(B=\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)