a/ \(=\sqrt{81-2.9.\sqrt{3}+3}=\sqrt{\left(9-\sqrt{3}\right)^2}=9-\sqrt{3}\)
b/ \(=\frac{1}{\sqrt{2}}.\sqrt{14-6\sqrt{5}}=\frac{1}{\sqrt{2}}.\sqrt{9-2.3.\sqrt{5}+5}=\frac{1}{\sqrt{2}}\sqrt{\left(3-\sqrt{5}\right)^2}\)
\(=\frac{3-\sqrt{5}}{\sqrt{2}}=\frac{3\sqrt{2}-\sqrt{10}}{2}\)
c/ Ko khai phương được
Giải các phương trình sau..:
a,\(4\sqrt{4x-8}-2\sqrt{9x-18}+\sqrt{16x-32}=5\)
b,\(\sqrt{x^2+6x+9}-2=7\)
Thực hiện phép tính:
a. \(2\sqrt{2}-3\sqrt{18}+4\sqrt{32}-2\sqrt{50}\)
b. \(\sqrt{6+2\sqrt{5}}+\sqrt{\left(\sqrt{5}-7\right)^2}\)
c. \(\dfrac{1}{2-\sqrt{6}}-\dfrac{1}{2+\sqrt{6}}\)
Rút gọn:
a) \(2\sqrt{98}-3\sqrt{18}+\dfrac{1}{2}\sqrt{32}\)
b)\(\left(5\sqrt{2}+2\sqrt{5}\right).\sqrt{5}-\sqrt{250}\)
c)\(\left(2\sqrt{3}-5\sqrt{2}\right).\sqrt{3}-\sqrt{36}\)
d)\(3\sqrt{48}+2\sqrt{27}-\dfrac{1}{3}\sqrt{243}\)
e) \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}\)
f)\(4\sqrt{\dfrac{1}{2}}-\dfrac{6}{\sqrt{2}}\dfrac{2}{\sqrt{2}+1}\)
Rút gọn:
a.\(\sqrt{21-6\sqrt6}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)
b.\(\sqrt{4+\sqrt{15}}-\sqrt{7-3\sqrt{5}}\)
c.\(\sqrt{\dfrac{13}{4}+\sqrt{3}}\)\(-\sqrt{\dfrac{7}{4}-\sqrt{3}}\)
rút gọn biểu thức
a, \(\dfrac{1}{\sqrt{7-\sqrt{24}+1}}-\dfrac{1}{\sqrt{7+\sqrt{24}+1}}\)
b,\(\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}+\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}\)
c,\(\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4}+\sqrt{7}}+\dfrac{4-\sqrt{7}}{3\sqrt{7}-\sqrt{4}-\sqrt{7}}\)
Thực hiện phép tính:
a)\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
b)\(\dfrac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+\sqrt{11}}}-\sqrt{3-2\sqrt{2}}\)
c)\(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
Tính:
a) \(A=\sqrt{8-2\sqrt{15}}\left(\sqrt{3}+\sqrt{5}\right)-\left(\sqrt{45}-\sqrt{20}\right)\)
b) \(B=\left(\frac{\sqrt{21}-\sqrt{3}}{\sqrt{7}-1}-\frac{\sqrt{15}-\sqrt{3}}{1-\sqrt{5}}\right)\left(\frac{1}{2}\sqrt{6}-\sqrt{\frac{3}{2}}+3\sqrt{\frac{2}{3}}\right)\)
c) \(C=2\sqrt{3}+\sqrt{7-4\sqrt{3}}+\left(\sqrt{\frac{1}{3}}-\sqrt{\frac{4}{3}+}\sqrt{3}\right):\sqrt{3}\)
d) \(D=\left(\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}\right):\frac{1}{\sqrt{7-4\sqrt{3}}}\)
Thực hiện phép tính
a,\(\sqrt{2}.\sqrt{98}\)
b,\(\sqrt{75}:\sqrt{3}\)
c,\(\sqrt{\left(3-\sqrt{11}\right)^2}\)
d,\(\left(2\sqrt{7}+4\sqrt{3}\right).\sqrt{3}-\sqrt{84}\)
Thực hiện phép tính:
a,\(\sqrt{2}.\sqrt{98}\)
b,\(\sqrt{75}:\sqrt{3}\)
c,\(\sqrt{\left(3-\sqrt{11}\right)^2}\)
d,\(\left(2\sqrt{7}+4\sqrt{3}\right).\sqrt{3}-\sqrt{84}\)
