Bài 2: Căn thức bậc hai và hằng đẳng thức căn bậc hai của bình phương
Các câu hỏi tương tự
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)\(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=2\)
1. \(\sqrt{\left(5+\sqrt{7}\right)^2}-\sqrt{8-2\sqrt{7}}\) .
2. \(\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{4-2\sqrt{3}.}\)
3. \(\sqrt{11}-\sqrt{20-6\sqrt{11}}=3\)
4.\(\sqrt{41+12\sqrt{5}}-\sqrt{41-12\sqrt{5}}=2\sqrt{5.}\)
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) \(\left(1+\sqrt{2021}\right)\sqrt{2022-2\sqrt{2021}}\)
Chứng minh:
a)\(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
b)\(8-2\sqrt{7}=\left(\sqrt{7}-1\right)^2\)
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)\(\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right).2\sqrt{6}\)
a) \(\sqrt{5+2\sqrt{6}}-\sqrt{3-2\sqrt{2}}\)
b) \(\sqrt{11+6\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)
c) \(\sqrt{2}\sqrt{2-\sqrt{3}}\left(\sqrt{3}+1\right)\)
CMR:
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
c) \(23-8\sqrt{7}=\left(4-\sqrt{7}\right)^2\)
d) \(\sqrt{17-12\sqrt{2}}+2\sqrt{2}=3\)
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)\(\left(3\sqrt{2}+1\right)\left(2\sqrt{3}+1\right)\left(6\sqrt{6}+1\right)\left(215-34\sqrt{3}-33\sqrt{2}\right)\)
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 ) \(\left(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\sqrt{200}\right):\frac{1}{8}\)