Đặt \(A=\sqrt{\sqrt{3}+\sqrt{2}}+\sqrt{\sqrt{3}-\sqrt{2}}\Rightarrow A>0\)
\(A^2=2\sqrt{3}+2\sqrt{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}=2\sqrt{3}+2\)
\(\Rightarrow A=\sqrt{2\sqrt{3}+2}\)
Rút gọn biểu thức:
a) \(\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)
b) \(\sqrt{6-2\sqrt{3+\sqrt{13+4\sqrt{3}}}}\)
c) \(\sqrt{\sqrt{3}+\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
d) \(\sqrt{23-6\sqrt{10+4\sqrt{3-2\sqrt{2}}}}\)
Rút gọn các biểu thức sau:
D = \(\sqrt{9+4\sqrt{2}}-3\)
E = \(\sqrt{4+2\sqrt{3}}-\sqrt{13+4\sqrt{3}}\)
F = \(\sqrt{7-4\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
Rút gọn :
a) \(\dfrac{3\sqrt{2-6}}{\sqrt{2-1}}\)
b) \(\dfrac{3\sqrt{5}+5\sqrt{3}}{\sqrt{3}+\sqrt{5}}\)
c) \(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\)
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=\(\dfrac{2}{x^2-y^2}\cdot\sqrt{\dfrac{9\left(x^2+2xy+y^2\right)}{4}}\) \(\left(vớix\ne y,x\ne-y\right)\)
B3: Rút gọn :
a, \(\sqrt{3}+\sqrt{8-2\sqrt{5}}\)
b, \(\sqrt{x-1-2\sqrt{x-2}}\)
Rút gọn :
a) \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
b) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Rút gọn : \(A=\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}-\sqrt{2\sqrt{2}+2}\)
rút gọn hoạc tính giá trị các biểu thức sau
1)1+\(\sqrt{\dfrac{\left(x-1\right)^2}{x-1}}\)
2)\(\sqrt{\left(x-2\right)^2}+\dfrac{x-2}{\sqrt{\left(x-2\right)^2}}\)
3)\(\sqrt{m}-\sqrt{m-2\sqrt{m}+1}\)
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 biểu thức
A=\(\sqrt{27}\)-2\(\sqrt{12}\)-\(\sqrt{75}\)
