Chương I - Căn bậc hai. Căn bậc ba
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TG
18 tháng 6 2021 lúc 15:18
Tính GTBT: \(M=\left(x-y\right)^3+3\left(x-y\right)\left(xy+1\right)\) biết
\(x=\sqrt[3]{3+2\sqrt{2}}-\sqrt[3]{3-2\sqrt{2}}\)
\(y=\sqrt[3]{17+12\sqrt{2}}-\sqrt[3]{17-12\sqrt{2}}\)
Tính thu gọn :
a , sqrt{17-12sqrt{2}}-sqrt{17+12sqrt{2}}
b , sqrt{27+12sqrt{5}}-sqrt{27-12sqrt{5}}
c , sqrt{15-6sqrt{6}}+sqrt{15+sqrt{6sqrt{6}}}
d , sqrt{4+sqrt{15}}+sqrt{4-sqrt{15}}-2sqrt{3-sqrt{5}}
e , sqrt{17-3sqrt{32}}+sqrt{17+3sqrt{32}}
f , sqrt{5+sqrt{3-sqrt{29-12sqrt{5}}}}
Đọc tiếp
Tính thu gọn :
a , \(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
b , \(\sqrt{27+12\sqrt{5}}-\sqrt{27-12\sqrt{5}}\)
c , \(\sqrt{15-6\sqrt{6}}+\sqrt{15+\sqrt{6\sqrt{6}}}\)
d , \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
e , \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
f , \(\sqrt{5+\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
Thực hiện phép tính
a) \(\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{17}}\)
b) \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)
c) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
Tính giá trị các biểu thức sau:
a) Asqrt{frac{2+sqrt{3}}{2-sqrt{3}}}+sqrt{frac{2-sqrt{3}}{2+sqrt{3}}}
b) Afrac{sqrt{3-2sqrt{2}}}{sqrt{17-12sqrt{2}}}-frac{sqrt{3+2sqrt{2}}}{sqrt{17+12sqrt{2}}}
c) Afrac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}+frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}
c) Afrac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-frac{sqrt{5}+1}{sqrt{5}-1}
Đọc tiếp
Tính giá trị các biểu thức sau:
a) \(A=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}+\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}\)
b) \(A=\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
c) \(A=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)
c) \(A=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
Tính \(\dfrac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
Tính: \(\sqrt{17-3\sqrt{32}}+\sqrt{17-3\sqrt{32}}\)
Rút gọn:
a) sqrt{24-3sqrt{15}}-sqrt{36-9sqrt{15}}
b)sqrt{2-sqrt{3}}-sqrt{2+sqrt{3}}
c)sqrt{3-sqrt{5}}-sqrt{3+sqrt{5}}
d) sqrt{9-sqrt{17}}-sqrt{9+sqrt{17}}
e) sqrt{7+sqrt{13}}-sqrt{7-sqrt{13}}
f) sqrt{12-3sqrt{7}}-sqrt{12+3sqrt{7}}
Đọc tiếp
Rút gọn:
a) \(\sqrt{24-3\sqrt{15}}-\sqrt{36-9\sqrt{15}}\)
b)\(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
c)\(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
d) \(\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}\)
e) \(\sqrt{7+\sqrt{13}}-\sqrt{7-\sqrt{13}}\)
f) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
C/m A, B ∈ Z, với:
A= \(\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)
B= \(\dfrac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
Help me
Bài 1 : Rút gọn
a) \(\dfrac{2\sqrt{3}+2}{4\sqrt{3}+4}\) b) \(\dfrac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}\) c) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\) d) \(\sqrt{9+\sqrt{17}}\). \(\sqrt{9-\sqrt{17}}\)