a, \(\sqrt{75}+\sqrt{12}-\sqrt{ }3\)
b, \((2\sqrt{2}+\sqrt{5)}.\sqrt{2-\frac{1}{3}.}\sqrt{90}\)
c, \(\frac{1}{5-\sqrt{3}}-\frac{1}{5+\sqrt{3}}\)
Rút gọn biểu thức:
\(A=\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}\)
\(B=\left(\frac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\frac{4}{1+\sqrt{5}}+4\right)\)
\(C=\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right):\left(1:\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
\(D=2\sqrt{50}-\frac{1}{\sqrt{2}-1}+4\sqrt{\frac{9}{2}}-\sqrt{3-2\sqrt{2}}\)
1.Trục căn thức ở mẫu
\(\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
2.Rút gọn
a,\(\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}\)
b,\(\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}\)
c,\(\frac{1}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{3}-\sqrt{2}}-\frac{2}{\sqrt{5}+\sqrt{2}}\)
1. Tính:
a) \(\sqrt{243}-\frac{1}{2}\sqrt{12}-2\sqrt{75}+\sqrt{27}\)
b) \(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{5}{1+\sqrt{6}}-6\sqrt{\frac{1}{6}}\)
2. Rút gọn: \(\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)
rút gọn
A=\(\frac{1+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{1-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
Giúp mk vs
Rút gọn
a) \(A=\left(\frac{\sqrt{10}-\sqrt{5}}{\sqrt{8}-2}-\frac{\sqrt{90}}{3}\right).\frac{1}{\sqrt{5}}\)
b) \(B=\left(\frac{\sqrt{26}-\sqrt{13}}{1-\sqrt{2}}+\frac{\sqrt{18}-\sqrt{6}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{13}-\sqrt{6}}\)
c) \(C=\frac{\sqrt{10+2\sqrt{21}}-\sqrt{5-2\sqrt{6}}}{\sqrt{9-2\sqrt{14}}}\)
Thực hiện phép tính:
a,\(\frac{1}{2}\sqrt{48}-5\sqrt{27}+2\sqrt{147}-\sqrt{108}\)
b,\(\sqrt{\left(\sqrt{5}-3\right)^2}+\sqrt{\left(1+\sqrt{5}\right)^2}\)
c,\(\frac{12}{3+\sqrt{3}}-\frac{6}{\sqrt{3}}+\frac{\sqrt{27}-3\sqrt{2}}{\sqrt{3}-\sqrt{2}}\)
d,\(\left(\sqrt{2+\sqrt{3}}-\sqrt{3+\sqrt{5}}\right)^2\)
Giúp mk vs huhu mk hứa sẽ tick ạ :>
B1: Rút gọn biểu thức sao
P=\(\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+...+\frac{1}{\sqrt{23}+\sqrt{25}}\)
B2: Cho số dương a,b,c thỏa mãn a>b. CMR \(\sqrt{a+c}-\sqrt{a}< \sqrt{b+c}-\sqrt{b}\)
rút gọn \(\frac{1}{2-\sqrt{5}}+\frac{2}{\sqrt{5}+\sqrt{3}}:\frac{1}{\sqrt{21-12\sqrt{3}}}\)
\(\frac{5\sqrt{3}}{\sqrt{3}-\sqrt{5}-\sqrt{3}}-\frac{5\sqrt{3}}{\sqrt{3-\sqrt{5}}+\sqrt{3}}\)
