\(\dfrac{5+7\sqrt{5}}{\sqrt{5}}+\dfrac{11+\sqrt{11}}{1+\sqrt{11}}=\dfrac{\sqrt{5}\left(\sqrt{5}+7\right)}{\sqrt{5}}+\dfrac{\sqrt{11}\left(1+\sqrt{11}\right)}{1+\sqrt{11}}=\sqrt{5}+7+\sqrt{11}\)
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) \(\left(1+\sqrt{2021}\right)\sqrt{2022-2\sqrt{2021}}\)
Bài 1 :
a, \(\dfrac{1}{2}\sqrt{12}+\sqrt{27}-\sqrt{75}\)
b, \(\sqrt{7-4\sqrt{3}}-\sqrt{4+2\sqrt{3}}\)
c, 6\(\sqrt{27}-2\sqrt{75}-\dfrac{1}{2}\sqrt{300}\)
d, \(\dfrac{7}{\sqrt{10}-\sqrt{3}}-\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}-\dfrac{6}{\sqrt{3}}\)
e, \(\sqrt{\dfrac{\sqrt{5}}{8\sqrt{5}+3\sqrt{35}}}.(3\sqrt{2}+\sqrt{14)}\)
f, \(\sqrt{11-4\sqrt{ }7}+\dfrac{2\sqrt{7}-2}{\sqrt{7}-1}\)
g, \((\sqrt{125}-3\sqrt{3})\dfrac{\sqrt{5}-\sqrt{3}}{8+\sqrt{15}}\)
h, \(\sqrt{100}-\sqrt{64}\)
i, \(\sqrt{(1-\sqrt{3})^2}-\sqrt{3}\)
Bạn nào biết làm bài này thì giúp mình với ạ ! sáng mai mình cần gấp !
a,\(\sqrt{22+12\sqrt{2}}\)
b,\(\sqrt{\dfrac{5+2\sqrt{6}}{2}}\)
c,\(\sqrt{30+4\sqrt{2}\sqrt{7}}\)
d,\(\sqrt{5+2\sqrt{2-\sqrt{9-4\sqrt{2}}}}\)
e,\(\sqrt{1+2\sqrt{\sqrt{2+\sqrt{11+6\sqrt{2}}}}}\)
f,\(\sqrt{1+\dfrac{\sqrt{3}}{2}+\sqrt{1-\dfrac{\sqrt{3}}{2}}}\)
g,\(\sqrt{10-2\sqrt{21}}+\sqrt{4+2\sqrt{3}}\)
1. \(\sqrt{\left(5+\sqrt{7}\right)^2}-\sqrt{8-2\sqrt{7}}\) .
2. \(\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{4-2\sqrt{3}.}\)
3. \(\sqrt{11}-\sqrt{20-6\sqrt{11}}=3\)
4.\(\sqrt{41+12\sqrt{5}}-\sqrt{41-12\sqrt{5}}=2\sqrt{5.}\)
bài 1 tính
a, \(\sqrt{\left(1-\sqrt{5}\right)^2}+1\)
b, \(\sqrt{3+2\cdot\sqrt{2}}-2\)
c, \(\sqrt{b^2-b+\dfrac{1}{4}}-\left(2b-\dfrac{1}{2}\right)\left(vsb\ge\dfrac{1}{2}\right)\)
d, \(\sqrt{7+2\cdot\sqrt{10}}\)
e. \(\sqrt{11-4\cdot\sqrt{7}}\)
f, \(\sqrt{x-2\cdot\sqrt{x-1}}\)
g, \(3x+\sqrt{x^2-2x+1}\)
h, \(\sqrt{y+2\sqrt{y^2-2y+1}}\) (voi y>1)
i, \(\sqrt{17-2\sqrt{32}}+\sqrt{17+2\sqrt{32}}\)
k, \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
a) \(\sqrt{11-x}+\sqrt{x-5}\)
b) \(\sqrt{x^2-2x+3}\)
c) \(\sqrt{2x-3}+\dfrac{1}{2x-5}\)
d)\(\sqrt{2-a}+\dfrac{1}{a}\)
2/tính
a) \(\sqrt{17-12\sqrt{2}}-2\sqrt{2}\)
b) \(\sqrt{15-6\sqrt{6}}+\sqrt{6}\)
Rút gọn
a.\(\dfrac{\sqrt{7}-5}{2}-\dfrac{6}{\sqrt{7}-2}+\dfrac{1}{3+\sqrt{7}}+\dfrac{3}{5+2\sqrt{7}}\)
b.\(\left(\sqrt{10}+\sqrt{2}\right).\left(6-2\sqrt{5}\right).\sqrt{3+\sqrt{5}}\)
Rút gọn
A=\(\sqrt{13+4\sqrt{10}}\)
B= \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
C= \(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-\sqrt{7}}\)
Bài 2: Tìm sự xác định của các biểu thức chứa căn
1> \(\sqrt{6x+1}\)
2> \(\sqrt{\dfrac{-3}{2+x}}\)
3> \(\sqrt{-8x}\)
4> \(\sqrt{4-5x}\)
5> \(\sqrt{\left(x+5\right)^2}\)
6> \(\sqrt{\dfrac{\sqrt{6}-4}{m+2}}\)
7> \(\sqrt{\left(\sqrt{3}-x\right)^2}\)
8> \(\dfrac{16x-1}{\sqrt{x}-7}\)
9> \(\sqrt{x^2+2x+1}\)
10> \(\sqrt{2x+5}\)
11> \(\sqrt{-12x+5}\)
12> \(\dfrac{3}{\sqrt{12x-1}}\)
13> 2 - \(4\sqrt{5x+8}\)
14> \(\sqrt{x^2+3}\)
15> \(\sqrt{\dfrac{5}{x^2}}\)
16> \(\sqrt{\dfrac{x+3}{7-x}}\)
17> \(\sqrt{x-x^2}\)
