\(a,VT=9+4\sqrt{5}=\sqrt{5^2}+2.2\sqrt{5}+2^2=\left(\sqrt{5}+2\right)^2=VP\left(dpcm\right)\)
\(b,\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
\(\Leftrightarrow\sqrt{9-4\sqrt{5}}=\sqrt{5}-2\)
Ta có : \(VT=\sqrt{9-4\sqrt{5}}=\sqrt{\sqrt{5^2}-2.2\sqrt{5}+2^2}=\sqrt{\left(\sqrt{5}-2\right)^2}=\left|\sqrt{5}-2\right|=\sqrt{5}-2=VP\left(dpcm\right)\)
CMR:
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
c) \(23-8\sqrt{7}=\left(4-\sqrt{7}\right)^2\)
d) \(\sqrt{17-12\sqrt{2}}+2\sqrt{2}=3\)
Chứng minh :
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
c) \(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
d) \(\sqrt{23+8\sqrt{7}}-\sqrt{7}=4\)
Tính:
a) \(\left(\sqrt{1\dfrac{9}{16}}-\sqrt{\dfrac{9}{16}}\right):5\)
b) \(\left(\sqrt{3}-2\right)^2\left(\sqrt{3}+2\right)^2\)
c) \(\left(11-4\sqrt{3}\right)\left(11+4\sqrt{3}\right)\)
d) \(\left(\sqrt{2}-1\right)^2-\dfrac{3}{2}\sqrt{\left(-2\right)^2}+\dfrac{4\sqrt{2}}{5}+\sqrt{1\dfrac{11}{25}}.\sqrt{2}\)
e) \(\left(1+\sqrt{2021}\right)\sqrt{2022-2\sqrt{2021}}\)
Câu1: Rút gọn
\(a,x+\sqrt{\left(x+2\right)^2}\cdot\left(x-2\right)\\ b,\sqrt{m^2-6m+9-2m}\left(x>3\right)\\ c,1+\sqrt{\frac{\left(x-1\right)^2}{x-1}}\\ d,\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}\)
Câu 2: So sánh
\(a,3và\sqrt{5}\\ \\ \\ b,2\sqrt{2}và3\sqrt{2}\\ \\ \\ c,-4\sqrt{5}và-6\sqrt{6}\\ \\ \\ d,2\sqrt{3}-5và\sqrt{3}-4\\ \\ \\e,A=\sqrt{2006}-\sqrt{2005}và\\ B=\sqrt{2005}-\sqrt{2004}\)
Câu 3: Rút gọn
\(a,\sqrt{16-2\sqrt{55}}\\ \\ \\ \\ \\ \\ \\ \\ \\ b,\sqrt{14-6\sqrt{5}}\\ \\ \\ \\ \\ \\ \\ \\ \\ c,\sqrt{36+12\sqrt{5}}\\ \\ \\ \\ \\ \\ \\ \\ \\ d,\sqrt{29+12\sqrt{5}}\)
Câu4: Tìm đkxđ
\(a,\sqrt{x^2-9}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ b,\sqrt{x^2-3x+2}\)
\(c,\frac{\sqrt{x+3}}{\sqrt{5-x}}\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ d,\sqrt{\frac{x+3}{5-x}}\)
Giải hộ ạ!!
a. \(\sqrt{23+8\sqrt{7}}-\sqrt{7}\)
b.\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
c. \(\sqrt{\left(3-\sqrt{5}\right)^2}-\sqrt{\left(1-\sqrt{5}\right)^2}\)
e) \(\left(3+\sqrt{2}\right)\sqrt{11+6\sqrt{2}}\)
f) \(\left(2-\sqrt{5}\right)\sqrt{9+4\sqrt{5}}\)
Tính giá trị các biểu thức sau:
\(A=\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
\(B=\left(11-4\sqrt{3}\right)\left(11+4\sqrt{3}\right)\)
\(C=\sqrt{4-2\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)
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.\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
a) \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
b)\(\sqrt{\left(\sqrt{2-3}\right)^2}.\sqrt{11+6\sqrt{2}}\)
c) \(\sqrt{\left(\sqrt{3-3}\right)^2.}\sqrt{\frac{1}{3-\sqrt{3}}}\)
d)\(\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right).2\sqrt{6}\)
