\(\Leftrightarrow C=\left(\sqrt{\left(\sqrt{5}+\sqrt{6}\right)^2}-\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}\right)\left(\sqrt{5}+\sqrt{2}\right)\)
\(\Leftrightarrow C=\left(\sqrt{5}+\sqrt{6}-\sqrt{6}+\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)\)
\(\Leftrightarrow C=\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)\)
\(\Leftrightarrow C=\left(\sqrt{5}+\sqrt{2}\right)^2\)
Rút gọn
1) \(E=\left(\sqrt{11}-3\right)\left(\sqrt{13-\sqrt{6}+2\sqrt{30-\sqrt{54}}}+\sqrt{11}-\sqrt{10-\sqrt{6}}\right)\)
2) \(F=\frac{\left(\sqrt{3-\sqrt{5}}-1\right)\left(\sqrt{3-\sqrt{5}}\left(3-\sqrt{5}\right)+1\right)}{4-\sqrt{5}-\sqrt{3-\sqrt{5}}}+\sqrt{5}\)
RÚT GỌN BIỂU THỨC
A= \(\left(2+\dfrac{5-2\sqrt{5}}{2-\sqrt{5}}\right)\)\(\left(2+\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}\right)\)
B= \(\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)\)\(\left(\sqrt{6}+11\right)\)
Bài 1: Rút gọn
a. \(\left(5-2\sqrt{3}\right)^2+\left(5+2\sqrt{3}\right)^2\)
b. \(\left(\sqrt{5}+\sqrt{2}\right)^2-\left(2\sqrt{5}+1\right)\left(2\sqrt{5}-1\right)-\sqrt{40}\)
c. \(\left(\sqrt{2}-1\right)^2-\frac{2}{3}\sqrt{4}+\frac{4\sqrt{2}}{5}+\sqrt{1\frac{11}{15}}-\sqrt{2}\)
d. \(\left(\sqrt{6}-\sqrt{18}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right)2\sqrt{6}+2\sqrt{3}\)
e. \(\left(2\sqrt{3}-3\sqrt{2}\right)^2+6\sqrt{6}+3\sqrt{24}\)
Bài 2: Rút gọn
A =\(\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x}-1}:\frac{\sqrt{x+1}}{x-2\sqrt{x}+1}\right)\)(x>0 ; x khác 1)
Rút gọn các biểu thức sau:
a. \(\dfrac{8}{\left(\sqrt{5}+\sqrt{3}\right)^2}\) - \(\dfrac{8}{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
b.\(\dfrac{1}{4-3\sqrt{2}}\) - \(\dfrac{1}{4+3\sqrt{2}}\)
c.\(\left(\dfrac{\sqrt{7}+3}{\sqrt{7}-3}-\dfrac{\sqrt{7}-3}{\sqrt{7}+3}\right)\): \(\sqrt{28}\)
d.\(\dfrac{3}{\sqrt{6}-\sqrt{3}}\)+\(\dfrac{4}{\sqrt{7}+\sqrt{3}}\)
Rút gọn các biểu thức sau
a) 2\(\sqrt{32}\) + 3\(\sqrt{72}-7\sqrt{50}+\sqrt{2}\) b)\(\sqrt{\left(3-\sqrt{3}\right)^2}+\sqrt{\left(2-\sqrt{3}\right)^2}\) c) \(\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)
d) \(x-4+\sqrt{16-8x+x^2}\left(x>4\right)\) e) \(\dfrac{1}{a-b}\sqrt{a^4\left(a-b\right)^2}vớia< b\)
Rút gọn:
A = \(\left(\sqrt{11}-\sqrt{3}\right)\left(\sqrt{13-\sqrt{6}+2\sqrt{30-\sqrt{54}}}+\sqrt{11}-\sqrt{10-\sqrt{6}}\right)\)
RÚT GỌN
D=\(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
N=\(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)\)
C=\(\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{8-2\sqrt{15}}\right)\)
M=\(\sqrt{5-2\sqrt{6}}-\sqrt{5+2\sqrt{6}}\)
Rút gọn: (Giải chi tiết từng bước)
7) \(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)
8) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
rút gọn
g, \(\left(\dfrac{5-2\sqrt{5}}{2-\sqrt{5}}-2\right).\left(\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}-2\right)\) h,\(\left(\dfrac{4}{3}\sqrt{3}+\sqrt{2}+\sqrt{3\dfrac{1}{3}}\right).\left(\sqrt{1,2}+\sqrt{2}-4\sqrt{\dfrac{1}{5}}\right)\)
