\(\sqrt{m+2\sqrt{m-1}}+\sqrt{m-2\sqrt{m-1}}\)
=\(\sqrt{\left(\sqrt{m-1}\right)^2+2\sqrt{m-1}+1}+\sqrt{\left(\sqrt{m-1}\right)^2-2\sqrt{m-1}+1}\)
=\(\sqrt{\left(\sqrt{m-1}+1\right)^2}+\sqrt{\left(\sqrt{m-1}-1\right)^2}\)
=\(\sqrt{m-1}+1+\sqrt{m-1}-1=2\sqrt{m-1}\)
rút gọn biểu thức
A=2\(\sqrt{27}\)+5\(\sqrt{12}\)-3\(\sqrt{48}\)
B=\(\sqrt{147}\)+\(\sqrt{75}\)-4\(\sqrt{27}\)
C=3\(\sqrt{2}\)(4-\(\sqrt{2}\))+3(1-2\(\sqrt{2}\))2
D=2\(\sqrt{5}\)-\(\sqrt{125}\)-\(\sqrt{80}\)+\(\sqrt{605}\)
Rút gọn biểu thức
a)\(\dfrac{3}{\sqrt{5}-\sqrt{2}}+\dfrac{4}{\sqrt{6}+\sqrt{2}}+\dfrac{3}{\sqrt{6}+\sqrt{5}}\)
b)\(\dfrac{3}{\sqrt{5}-\sqrt{2}}-\dfrac{1}{\sqrt{5-\sqrt{24}}}-\dfrac{\sqrt{2}}{\sqrt{4+\sqrt{15}}}\)
Help me plsssssssssssssss
Rút gọn biểu thức
A= \(\sqrt{\left(2-\sqrt{3}\right)^2}\)+\(\sqrt{3}\)
B=\(\sqrt{6+2\sqrt{5}}\)-\(\sqrt{6-2\sqrt{5}}\)
Rút gọn
a)\(\sqrt{m+2\sqrt{m-1}}-\sqrt{m-2\sqrt{m-1}}\left(m>2\right)\)
b)\(\sqrt{x-1-2\sqrt{x-2}}+\sqrt{\sqrt{x-1+2\sqrt{x-2}}}\)
c)\(\sqrt{x+3+4\sqrt{x-1}}+\sqrt{x+8-8\sqrt{x-1}}\left(1< x< 10\right)\)
d)\(\sqrt{2m+4+6\sqrt{2m-5}}+\sqrt{2m-4-2\sqrt{2m-5}}\)
C/M đẳng thức
a, \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}=\sqrt{2}\)
b, \(\frac{\sqrt{1+\frac{2\sqrt{2}}{3}}+\sqrt{1-\frac{2\sqrt{2}}{3}}}{\sqrt{1+\frac{2\sqrt{2}}{3}}-\sqrt{1-\frac{2\sqrt{2}}{3}}}=\sqrt{2}\)
RÚT GỌN BIỂU THỨC
A= \(\left(2+\dfrac{5-2\sqrt{5}}{2-\sqrt{5}}\right)\)\(\left(2+\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}\right)\)
B= \(\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)\)\(\left(\sqrt{6}+11\right)\)
Rút gọn các biểu thức
a)\(\dfrac{\sqrt{a}}{\sqrt{a}-3}-\dfrac{3}{\sqrt{a}+3}-\dfrac{a-2}{a-9}\)
b)\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
Help me !!!
1. Tìm giá trị nhỏ nhất của M:
M = \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+15+8\sqrt{x-1}}\)
2. Rút gọn:
A= \(\sqrt{\sqrt{28-16\sqrt{3}}}-\sqrt{\sqrt{28+16\sqrt{3}}}\)
B= \(\sqrt{5-2\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
Rút gọn: \(M=\dfrac{8}{\sqrt{5}-\sqrt{3}}+\dfrac{7}{\sqrt{3}-2}+\dfrac{4}{\sqrt{2}-1}+\dfrac{3\sqrt{5}-\sqrt{15}}{\sqrt{15}}\)
