\(A=9\sqrt{2}+7\sqrt{2}-12\sqrt{2}=4\sqrt{2}\)
\(B=\sqrt{2}-1-\sqrt{\left(3+\sqrt{2}\right)^2}=\sqrt{2}-1-3-\sqrt{2=-4}\)
Đúng 0
Bình luận (0)
Bài 2: Căn thức bậc hai và hằng đẳng thức căn bậc hai của bình phương
Các câu hỏi tương tự
a) \(\sqrt{5+2\sqrt{6}}-\sqrt{3-2\sqrt{2}}\)
b) \(\sqrt{11+6\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)
c) \(\sqrt{2}\sqrt{2-\sqrt{3}}\left(\sqrt{3}+1\right)\)
Bài 1 :Chứng minh các đẳng thức :
a ) 2sqrt{2}left(sqrt{3}-2right) + left(1+2sqrt{2}right)^2-2sqrt{6}9
b ) sqrt{2+sqrt{3}}+sqrt{2-sqrt{3}}sqrt{6}
c ) sqrt{11-6sqrt{2}}+sqrt{11+6sqrt{2}}6
Bài 2 : Rút gọn các biểu thức sau :
a ) frac{1}{sqrt{5}+sqrt{3}}-frac{1}{sqrt{5}-sqrt{3}}
b ) frac{sqrt{4-2sqrt{3}}}{sqrt{6}-sqrt{2}}
c ) frac{1}{2+sqrt{3}}+frac{sqrt{2}}{sqrt{6}}-frac{2}{3+sqrt{3}}
Bài 3 : Rút gọn các biểu thức sau :
a ) sqrt{20}-sqrt{45}+3sqrt{18}+sqrt{72}
b ) left(sqrt{28}-2sqrt{3}+sqrt{7}...
Đọc tiếp
Bài 1 :Chứng minh các đẳng thức :
a ) \(2\sqrt{2}\left(\sqrt{3}-2\right)\) + \(\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
b ) \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}=\sqrt{6}\)
c ) \(\sqrt{11-6\sqrt{2}}+\sqrt{11+6\sqrt{2}}=6\)
Bài 2 : Rút gọn các biểu thức sau :
a ) \(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\)
b ) \(\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{6}-\sqrt{2}}\)
c ) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)
Bài 3 : Rút gọn các biểu thức sau :
a ) \(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)
b ) \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{84}\)
c ) \(\left(\sqrt{6}+\sqrt{5}\right)^2-\sqrt{120}\)
d ) \(\left(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\sqrt{200}\right):\frac{1}{8}\)
a) \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
b)\(\sqrt{\left(\sqrt{2-3}\right)^2}.\sqrt{11+6\sqrt{2}}\)
c) \(\sqrt{\left(\sqrt{3-3}\right)^2.}\sqrt{\frac{1}{3-\sqrt{3}}}\)
d)\(\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right).2\sqrt{6}\)
1)chứng minh
a)\(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
b)\(\sqrt{11+6\sqrt{2}}+\sqrt{11-6\sqrt{2}}=6\)
2)chứng minh
a)\(8-2\sqrt{7}=\left(\sqrt{7}-1\right)^2\)
b)\(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=2\)
Tính:a) left(sqrt{1dfrac{9}{16}}-sqrt{dfrac{9}{16}}right):5b) left(sqrt{3}-2right)^2left(sqrt{3}+2right)^2c) left(11-4sqrt{3}right)left(11+4sqrt{3}right)d) left(sqrt{2}-1right)^2-dfrac{3}{2}sqrt{left(-2right)^2}+dfrac{4sqrt{2}}{5}+sqrt{1dfrac{11}{25}}.sqrt{2}e) left(1+sqrt{2021}right)sqrt{2022-2sqrt{2021}}
Đọc tiếp
Tính:
a) \(\left(\sqrt{1\dfrac{9}{16}}-\sqrt{\dfrac{9}{16}}\right):5\)
b) \(\left(\sqrt{3}-2\right)^2\left(\sqrt{3}+2\right)^2\)
c) \(\left(11-4\sqrt{3}\right)\left(11+4\sqrt{3}\right)\)
d) \(\left(\sqrt{2}-1\right)^2-\dfrac{3}{2}\sqrt{\left(-2\right)^2}+\dfrac{4\sqrt{2}}{5}+\sqrt{1\dfrac{11}{25}}.\sqrt{2}\)
e) \(\left(1+\sqrt{2021}\right)\sqrt{2022-2\sqrt{2021}}\)
Rút gọn :
dfrac{sqrt{x+sqrt{4left(x-1right)}}-sqrt{x-sqrt{4left(x-1right)}}}{sqrt{x^2-4left(x-1right)}}.left(sqrt{x-1}-dfrac{1}{sqrt{x-1}}right)
b)left(sqrt{2}+1right)left(sqrt{3}+1right)left(sqrt{6}+1right)left(5-2sqrt{2}-sqrt{3}right)
c)left(sqrt{5}+1right)left(sqrt{7}+1right)left(sqrt{35}+1right)left(34-4sqrt{7}-6sqrt{5}right)
d) left(sqrt{7}+1right)left(2sqrt{2}-1right)left(2sqrt{14}-1right)left(55+12sqrt{2}-7sqrt{7}right)
e)left(3sqrt{2}+1right)left(2sqrt{3}+1right)left(6sqrt{6}+1...
Đọc tiếp
Rút gọn :
\(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
b)\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)
c)\(\left(\sqrt{5}+1\right)\left(\sqrt{7}+1\right)\left(\sqrt{35}+1\right)\left(34-4\sqrt{7}-6\sqrt{5}\right)\)
d) \(\left(\sqrt{7}+1\right)\left(2\sqrt{2}-1\right)\left(2\sqrt{14}-1\right)\left(55+12\sqrt{2}-7\sqrt{7}\right)\)
e)\(\left(3\sqrt{2}+1\right)\left(2\sqrt{3}+1\right)\left(6\sqrt{6}+1\right)\left(215-34\sqrt{3}-33\sqrt{2}\right)\)
Rút gọn :
a) left(sqrt{6}+sqrt{2}right).left(sqrt{3}-2right)left(sqrt{2+sqrt{3}}right)
b) sqrt{2}.left(sqrt{2-sqrt{3}}right).left(sqrt{3}+1right)
c) left(sqrt{10}-sqrt{6}right).left(sqrt{4-sqrt{15}}right)
d)left(sqrt{3}-sqrt{12}right).left(sqrt{5+2sqrt{6}}right)
e) sqrt{2-sqrt{3}}.left(sqrt{6}-sqrt{2}right).left(2+sqrt{3}right)
f) sqrt{4+sqrt{5sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}}
Đọc tiếp
Rút gọn :
a) \(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right)\left(\sqrt{2+\sqrt{3}}\right)\)
b) \(\sqrt{2}.\left(\sqrt{2-\sqrt{3}}\right).\left(\sqrt{3}+1\right)\)
c) \(\left(\sqrt{10}-\sqrt{6}\right).\left(\sqrt{4-\sqrt{15}}\right)\)
d)\(\left(\sqrt{3}-\sqrt{12}\right).\left(\sqrt{5+2\sqrt{6}}\right)\)
e) \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}-\sqrt{2}\right).\left(2+\sqrt{3}\right)\)
f) \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
rút gọn biểu thức
a) A 2sqrt{frac{1}{2}}+sqrt{18}
b) B frac{5+3sqrt{5}}{sqrt{5}}+frac{3+sqrt{3}}{sqrt{3}+1}-left(sqrt{5+3}right)
c) C frac{1}{x+sqrt{x}}+frac{2sqrt{x}}{x-1}-frac{1}{x-sqrt{x}}left(x0,xne1right)
d) D left(frac{sqrt{x}+2}{x+2sqrt{x}+1}-frac{sqrt{x-2}}{x-1}right)left(x+sqrt{x}right)left(x0,xne1right)
e) E frac{2+sqrt{3}}{sqrt{2}+sqrt{2+sqrt{3}}}+frac{2-sqrt{3}}{sqrt{2}-sqrt{2-sqrt{3}}}
Đọc tiếp
rút gọn biểu thức
a) A= \(2\sqrt{\frac{1}{2}}+\sqrt{18}\)
b) B= \(\frac{5+3\sqrt{5}}{\sqrt{5}}+\frac{3+\sqrt{3}}{\sqrt{3}+1}-\left(\sqrt{5+3}\right)\)
c) C= \(\frac{1}{x+\sqrt{x}}+\frac{2\sqrt{x}}{x-1}-\frac{1}{x-\sqrt{x}}\left(x>0,x\ne1\right)\)
d) D = \(\left(\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}-\frac{\sqrt{x-2}}{x-1}\right)\left(x+\sqrt{x}\right)\left(x>0,x\ne1\right)\)
e) E = \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Tính:
1.sqrt{left(sqrt{3}+sqrt{2}right)^2} 4.sqrt{left(sqrt{3}right)^2+2.left(sqrt{3}right).left(1right)+left(1right)^2}
2.sqrt{left(sqrt{5}-sqrt{6}right)^2} 5.sqrt{left(sqrt{5}right)^2+2.left(sqrt{5}right).left(sqrt{3}right)+left(sqrt{3}right)^2}
3.sqrt{left(2sqrt{2}+sqrt{3}right)^2}...
Đọc tiếp
Tính:
1.\(\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\) 4.\(\sqrt{\left(\sqrt{3}\right)^2+2.\left(\sqrt{3}\right).\left(1\right)+\left(1\right)^2}\)
2.\(\sqrt{\left(\sqrt{5}-\sqrt{6}\right)^2}\) 5.\(\sqrt{\left(\sqrt{5}\right)^2+2.\left(\sqrt{5}\right).\left(\sqrt{3}\right)+\left(\sqrt{3}\right)^2}\)
3.\(\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}\) 6.\(\sqrt{\left(\sqrt{6}\right)^2-2.\left(\sqrt{6}\right).\left(\sqrt{5}\right)+\left(\sqrt{5}\right)^2}\)