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.\(\dfrac{\sqrt{7}-5}{2}-\dfrac{6}{\sqrt{7}-2}+\dfrac{1}{3+\sqrt{7}}+\dfrac{3}{5+2\sqrt{7}}\)
b.\(\left(\sqrt{10}+\sqrt{2}\right).\left(6-2\sqrt{5}\right).\sqrt{3+\sqrt{5}}\)
Rút gọn:
a)\(\sqrt{\left(3-\sqrt{7}\right)^2}-\sqrt{\left(2\sqrt{7}-6\right)^2}\)
b)\(\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}-\sqrt{\left(2\sqrt{3}-3\sqrt{2}\right)^2}\)
1.\(\sqrt{\frac{129}{16}+\sqrt{2}}\)
2.\(\sqrt{\frac{289+4\sqrt{72}}{16}}\)
3. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
4.\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
5.\(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
6.\(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4-\sqrt{15}}\)
7.\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
Rút gọn biểu thức:
\(A=\sqrt{\left(2-\sqrt{7}\right)^2}+\left(\sqrt{7}-1\right)^2\)
\(B=3\sqrt{\left(1,5\right)^2}-4\sqrt{\left(3-\sqrt{2}\right)^2}\)
Thực hiện các phép tính
a) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2+\sqrt{3}}}\)
b) \(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right)\sqrt{\sqrt{3+2}}\)
c) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
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)\(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=2\)
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) \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
\(a,\sqrt{3+2\sqrt{2}}-\sqrt{2}\)
\(b,\sqrt{16-6\sqrt{7}}-2\sqrt{7}\)
\(c,\sqrt{30+12\sqrt{6}}+\sqrt{30-12\sqrt{6}}\)
\(d,\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
\(e,\sqrt{\left(-2\right)^6}+\sqrt{\left(-3\right)^4}\)