Bài 3: Liên hệ giữa phép nhân và phép khai phương
Các câu hỏi tương tự
CMR \(\dfrac{1}{4}\)<\(\dfrac{2-\sqrt{2+\sqrt{2+\sqrt{2+..............+\sqrt{2}}}}}{2-\sqrt{2+\sqrt{2+..............+\sqrt{2}}}}\)<\(\dfrac{3}{10}\)
A)sqrt{2-sqrt{3}}.left(sqrt{6}+sqrt{2}right)
B)left(sqrt{2}+1^{ }right)^3-left(sqrt{2}-1right)^3 C)dfrac{2sqrt{8}-sqrt{12}}{sqrt{18}-sqrt{48}}-dfrac{sqrt{5}+sqrt{27}}{sqrt{30}+sqrt{162}} D)sqrt{dfrac{2-sqrt{3}}{2+sqrt{3}}}+sqrt{dfrac{2+sqrt{3}}{2-sqrt{3}}} E)dfrac{sqrt{3-sqrt{5}}.left(3+sqrt{5}right)}{sqrt{10}+sqrt{2}} F)dfrac{1}{sqrt{2}+sqrt{2+sqrt{3}}}+dfrac{1}{sqrt{2}-sqrt{2-sqrt{3}}}
Đọc tiếp
A)\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
B)\(\left(\sqrt{2}+1^{ }\right)^3-\left(\sqrt{2}-1\right)^3\) C)\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\) D)\(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\) E)\(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\) F)\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Rút gọn các biểu thức sau :a,dfrac{sqrt{6}+sqrt{10}}{sqrt{21}+sqrt{35}}b,dfrac{sqrt{405}+3sqrt{27}}{3sqrt{3}+sqrt{45}}c,dfrac{sqrt{2}+sqrt{3}+sqrt{4}-sqrt{6}-sqrt{9}-sqrt{12}}{sqrt{2}+sqrt{3}+sqrt{4}}d, Ddfrac{2}{x^2-y^2}cdotsqrt{dfrac{9left(x^2+2xy+y^2right)}{4}} left(vớixne y,xne-yright)
Đọc tiếp
Rút gọn các biểu thức sau :
a,\(\dfrac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)
b,\(\dfrac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
c,\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
d, D=\(\dfrac{2}{x^2-y^2}\cdot\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\) \(\left(vớix\ne y,x\ne-y\right)\)
Tính
a) \(\sqrt{13-4\sqrt{2}}\)
b) \(2\sqrt{40\sqrt{12}}-2\sqrt{75}-3\sqrt{5\sqrt{48}}\)
c) \(\sqrt{1+\dfrac{1}{1^2}+\dfrac{2}{2^2}}+\sqrt{1+\dfrac{1}{2^2}+\dfrac{2}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{2}{4^2}}+...+\sqrt{1+\dfrac{1}{99^2}+\dfrac{2}{100^2}}\)
Rút gọn:
a)\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)
b) \(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
Rút gọn:
a)\(\dfrac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)
b)\(\dfrac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
c)\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
d)\(\dfrac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}\)
bài 1: rút gọn các biểu thức.
a) dfrac{xsqrt{x}+ysqrt{y}}{sqrt{x}+sqrt{y}}-(sqrt{x}-sqrt{y})^2
b) sqrt{dfrac{x-2sqrt{x}+1}{x+2sqrt{x}+1}}(xge0)
c) dfrac{x-1}{sqrt{y}-1}sqrt{dfrac{(y-2sqrt{y}+1)^2}{(x-1)^4}}(xne1,yne1,y0)
bài 2:rút gọn và tính.
a) sqrt{dfrac{sqrt{a}-1}{sqrt{b}+1}:}sqrt{dfrac{sqrt{b}-1}{sqrt{a}+1}với}a7,25;b3,25
b) sqrt{15a^2-8asqrt{15}+16}vớiasqrt{dfrac{3}{5}}+sqrt{dfrac{5}{3}}
c) sqrt{10a^2-4asqrt{10}+4}vớiasqrt{dfrac{2}{5}}+sqrt{dfrac{5}{2}}
d) sqrt{a^2+2sqrt{a^2-1}}-sq...
Đọc tiếp
bài 1: rút gọn các biểu thức.
a) \(\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})^2\)
b) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}(x\ge0)\)
c) \(\dfrac{x-1}{\sqrt{y}-1}\sqrt{\dfrac{(y-2\sqrt{y}+1)^2}{(x-1)^4}}(x\ne1,y\ne1,y>0)\)
bài 2:rút gọn và tính.
a) \(\sqrt{\dfrac{\sqrt{a}-1}{\sqrt{b}+1}:}\sqrt{\dfrac{\sqrt{b}-1}{\sqrt{a}+1}với}a=7,25;b=3,25\)
b) \(\sqrt{15a^2-8a\sqrt{15}+16}vớia=\sqrt{\dfrac{3}{5}}+\sqrt{\dfrac{5}{3}}\)
c) \(\sqrt{10a^2-4a\sqrt{10}+4}vớia=\sqrt{\dfrac{2}{5}}+\sqrt{\dfrac{5}{2}}\)
d) \(\sqrt{a^2+2\sqrt{a^2-1}}-\sqrt{a^2-2\sqrt{a^2-1}}(a=\sqrt{5})\)
bài 3: rút gọn các biểu thức.
a) \(\sqrt{9(x-5)^2}(x\ge5)\)
b) \(\sqrt{x^2.(x-2)^2}(x< 0)\)
c)\(\dfrac{\sqrt{108x^3}}{\sqrt{12x}}(x>0)\)
d)\(\dfrac{\sqrt{13x^4y^6}}{\sqrt{208x^6y^6}}(x< 0:y\ne0)\)
ai giúp mik vs ạ, cảm ơn !
BÀI 1 : THỰC HIỆN PHÉP TÍNH
a, \(\left(1+\sqrt{3}-\sqrt[2]{2}\right)\times\left(1+\sqrt{3}+\sqrt[2]{2}\right)\)
b, \(\left(\dfrac{3}{2}\times\sqrt{6}+2\times\sqrt{\dfrac{2}{3}}-4\times\sqrt{\dfrac{3}{2}}\right)\times\left(3\times\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)
BÀI 2 : rút gọn
B = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-2}}\)
bài 1 : rút gọn các biểu thức sau .
a, sqrt{4left(a-3right)^2}+2sqrt{a^2+4a+4}left(a -2right)
b, sqrt{dfrac{left(x-2right)^2}{left(3-2right)^2}}+dfrac{x^2-1}{x-3}left(x 3right)
c, 4x-sqrt{8}+dfrac{sqrt{x^3+2x^2}}{sqrt{x+2}}
bài 2 thực hiện phép tính :
a, sqrt{8-sqrt[2]{7}}timessqrt{8+sqrt[2]{7}}
b, sqrt{4+sqrt{8}+}+sqrt{2}+sqrt{2+sqrt{2}}timessqrt{2-sqrt{2+2}}
c, left(4+sqrt{15}right)timessqrt{10}-sqrt{6}timessqrt{4-sqrt{15}}
d, left(2+sqrt{3}right)^2-left(2-sqrt{3}right)timesleft(2+sqr...
Đọc tiếp
bài 1 : rút gọn các biểu thức sau .
a, \(\sqrt{4\left(a-3\right)^2}+2\sqrt{a^2+4a+4}\left(a< -2\right)\)
b, \(\sqrt{\dfrac{\left(x-2\right)^2}{\left(3-2\right)^2}}+\dfrac{x^2-1}{x-3}\left(x< 3\right)\)
c, \(4x-\sqrt{8}+\dfrac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\)
bài 2 thực hiện phép tính :\
a, \(\sqrt{8-\sqrt[2]{7}}\times\sqrt{8+\sqrt[2]{7}}\)
b, \(\sqrt{4+\sqrt{8}+}+\sqrt{2}+\sqrt{2+\sqrt{2}}\times\sqrt{2-\sqrt{2+2}}\)
c, \(\left(4+\sqrt{15}\right)\times\sqrt{10}-\sqrt{6}\times\sqrt{4-\sqrt{15}}\)
d, \(\left(2+\sqrt{3}\right)^2-\left(2-\sqrt{3}\right)\times\left(2+\sqrt{3}\right)\)