Lời giải:
\(B=\left(\frac{3}{\sqrt{3}-1}-\frac{52}{3\sqrt{3}-1}+\frac{4\sqrt{3}}{\sqrt{3}-1}\right)(5+3\sqrt{3})\)
\(=\frac{3(3+\sqrt{3}+1)-52+4\sqrt{3}(3+\sqrt{3}+1)}{3\sqrt{3}-1}(5+3\sqrt{3})\)
\(=\frac{-28+19\sqrt{3}}{3\sqrt{3}-1}(5+3\sqrt{3})\)
Biểu thức rút gọn xấu. Mình nghĩ bạn nên xem lại đề.
* rút gọn biểu thức:
a, \(\sqrt{\frac{3}{20}}+\sqrt{\frac{1}{60}}-2\sqrt{\frac{1}{15}}\)
b, \(\left(\frac{1}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{3}}\right).\sqrt{5}\)
c, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
d, \(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)
e, \(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{1\frac{1}{3}}\)
rút gọn biểu thức:
1/ \(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
2/ \(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\frac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
3/ \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(2+\sqrt{3}\right)\)
4/ \(\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
giúp minh với cần gấp lắm
J = \(\left(1+\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)\) . \(\left(1-\frac{2-\sqrt{2}}{1-\sqrt{2}}\right)\)
M = \(\frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\frac{1}{\sqrt{6}}\)
N = \(\frac{6}{1+\sqrt{7}}+\frac{1}{\sqrt{7}}\)
O = \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{1}{2-\sqrt{3}}\)
Q = \(\left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right).\left(\sqrt{5}-\sqrt{2}\right)\)
S = \(\frac{2}{\sqrt{5}+1}-\sqrt{\frac{2}{3-\sqrt{5}}}\)
Các thầy cô, các bạn giúp em với ạ. Em cảm ơn !
A) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)
b) \(\left(\frac{\sqrt{7}-\sqrt{14}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}+\sqrt{5}}\)
c) \(\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}\)
d) \(5\sqrt{2}+\sqrt{18}-\sqrt{98}-\sqrt{288}\)
e)\(\left(\frac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{3}+\sqrt{5}}\)
g)\(\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)
C1. Tính:
a) \(\left(3\sqrt{\frac{3}{5}}-\sqrt{\frac{5}{3}}+\sqrt{5}\right)2\sqrt{5}+\frac{2}{3}\sqrt{75}\)
b) \(\left(\sqrt{3}-1\right)^2-\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(-3\right)^2.3}\)
C2. Tính
P = \(\frac{a-b}{\sqrt{a}+\sqrt{b}}+\frac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}}\) , \(a\ge0,b\ge0,a\ne b\)
Q = \(\left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right).\left(\sqrt{5}-\sqrt{2}\right)\)
R = \(\frac{2}{7+4\sqrt{3}}+\frac{2}{7-4\sqrt{3}}\)
S = \(\frac{2}{\sqrt{5}+1}-\sqrt{\frac{2}{3-\sqrt{5}}}\)
T = \(\frac{4}{1-\sqrt{3}}-\frac{\sqrt{15}+\sqrt{3}}{1+\sqrt{5}}\)
1 .
a)\(A=\frac{2}{2\sqrt[3]{2}+2+\sqrt[3]{4}}\)
b)\(B=\frac{6}{2\sqrt[3]{2}-2+\sqrt[3]{4}}\)
c)C=\(\frac{2}{\sqrt[3]{4}+\sqrt[3]{2}+2}\)
2 .
a)\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
b)\(B=\frac{\left(5+2\sqrt{6}\right).\left(49-20\sqrt{6}\right).\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
c)C=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7}+4\sqrt{3}}}}\)
d)D=(\(\left(\sqrt{3}-1\right).\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
\(B=\left(\frac{\sqrt{x}+2}{\sqrt{x}-1}-\frac{\sqrt{x}+1}{\sqrt{x-3}}+\frac{3\sqrt{x}-1}{\left(\sqrt{x-1}\right)\left(\sqrt{x}-3\right)}\right):\left(1-\frac{1}{\sqrt{x}-1}\right)\)
a) Rút gọn biểu thức B
b) Tìm x \(\in\) Zđể B nhận giá trị nguyên
P=\(\left(\frac{\sqrt{x}-1}{3\sqrt{x}-1}-\frac{1}{3\sqrt{x}+1}+\frac{8\sqrt{x}}{9x-1}\right):\left(1-\frac{3\sqrt{x}-2}{3\sqrt{x}+1}\right)\)
a) Rút gọn P
b) Tìm x để P =\(\frac{6}{5}\)
