\(\left(2+\sqrt{5}+\sqrt{3}\right)\left(2+\sqrt{5}-\sqrt{3}\right)\)
\(=\left(2+\sqrt{5}\right)^2-\left(\sqrt{3}\right)^2\)
\(=9+4\sqrt{5}-3\)
\(=6+4\sqrt{5}\)
Tính :
a) A= \(\sqrt{\sqrt{3}+\sqrt{2}}.\sqrt{\sqrt{3}-\sqrt{2}}\)
b) B=\(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}\)
c) C= \(3-\sqrt{3-\sqrt{5}}\)
a)\(\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)
b) \(\sqrt{7+4\sqrt{3}}-\sqrt{4+2\sqrt{3}}\)
c) \(\sqrt{8+2\sqrt{7}}+\sqrt{8-2\sqrt{7}}\)
d)\(\sqrt{7+2\sqrt{10}}-\sqrt{3-2\sqrt{2}}\)
Rút gọn :
a) \(\dfrac{3\sqrt{2-6}}{\sqrt{2-1}}\)
b) \(\dfrac{3\sqrt{5}+5\sqrt{3}}{\sqrt{3}+\sqrt{5}}\)
c) \(\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\)
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)\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
1. Tính
a. \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b.\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
c.\(\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
1)Tính:
a)(\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\))\(^2\) b)\(\sqrt{2-\sqrt{3}-\sqrt{2+\sqrt{3}}}\) c)\(\frac{\sqrt{10}+\sqrt{6}}{2\sqrt{5}+\sqrt{12}}\) d)\(\sqrt{8-2\sqrt{15}-\sqrt{8+2\sqrt{15}}}\) e)\(\sqrt{\left(1-\sqrt{2007}\right)^2}.\sqrt{2008+2\sqrt{2007}}\)
Rút gọn:
a)\(\dfrac{\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a}}{ab-1}\)
b) \(\dfrac{2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}}\)
b1. Rút gọn
a)\(\frac{5\sqrt{6}+6\sqrt{5}}{\sqrt{5}+\sqrt{6}}\)
b) \(\frac{2\sqrt{7}-4\sqrt{3}}{3\sqrt{35}-6\sqrt{15}}\)
c) \(\frac{12\sqrt{10}-16\sqrt{14}}{6\sqrt{5}-8\sqrt{7}}\)
d) \(\frac{6\sqrt{6}-27}{2\sqrt{2}-3\sqrt{3}}\)
e) \(\frac{-4\sqrt{2}+3\sqrt{5}}{-2\sqrt{10}}\)
\(A=\left(3+\sqrt{5}\right).\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3}-\sqrt{5}\)
B=\(B=\left(\sqrt{10}+\sqrt{6}\right)\sqrt{8}-2\sqrt{15}\)
\(Cho\sqrt{8-a}+\sqrt{5+a}=5tinh\sqrt{\left(8-a\right)\left(5+a\right)}\)
\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}-\sqrt{12}\right).\left(2+\sqrt{3}\right)\)
\(\sqrt{2}.\sqrt{2-\sqrt{3}}.\left(\sqrt{3}+1\right)\)
\(\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
