\(A=\sqrt{7+\sqrt{33}}+\sqrt{7-\sqrt{33}}>0\)
\(\Rightarrow A^2=14+2\sqrt{7^2-33}\)
\(\Rightarrow A^2=14+2\sqrt{16}=22\)
\(\Rightarrow A=\sqrt{22}\)
Bài tập: Rút gọn biểu thức
a. \(A=\sqrt{5+\sqrt{21}}+\sqrt{5-\sqrt{21}}\)
b. \(B=\sqrt{7+\sqrt{33}}+\sqrt{7-\sqrt{33}}\)
thu gọn bth
a, \(\sqrt{33-12\sqrt{6}}+\sqrt{15+6\sqrt{6}}\)
b, \(\dfrac{\sqrt{99}}{\sqrt{11}}+\dfrac{\sqrt{28}}{\sqrt{7}}-\sqrt{\sqrt{81}}\)
Tính:
a) \(\left(2\sqrt{5}-\sqrt{7}\right).\left(2\sqrt{5}+\sqrt{7}\right)\)
b)\(\left(\sqrt{5-2\sqrt{6}}+\sqrt{2}\right).\sqrt{3}\)
c)\(\sqrt{7-4\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)
d)\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
e)\(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\)
g)\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}\)
1. Thu gọn : \(\sqrt{33-8\sqrt{7}}\)
2. Tìm x: \(\sqrt{4x}-3\sqrt{x}+2\sqrt{15x}=18\)
3. Rút gọn: B=\(\dfrac{1}{\sqrt{11-2\sqrt{30}}}-\dfrac{3}{7-2\sqrt{10}}\). Giúp mình với nha, mình đang cần rất gấp, gấp lắm luôn, cảm ơn
Rút gọn
1, \(3\sqrt{3}.\left(3+2\sqrt{6}-\sqrt{33}\right)\)
2, \(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
3, \(\left(2\sqrt{28}-3\sqrt{7}+5\sqrt{63}\right).\sqrt{112}\)
4, \(\left(5\sqrt{6}-4\sqrt{10}+7\sqrt{30}\right):\sqrt{2}\)
5, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
6, \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)
7, \(\left(4\sqrt{27}-2\sqrt{48}-5\sqrt{75}\right):2\sqrt{3}\)
Các bạn ơi ! giúp mik với đi !!!
Tính giá trị biểu thức:
\(M=\sqrt{\left(1-\sqrt{3}\right)^2}-3\sqrt{12}+\dfrac{\sqrt{33}}{\sqrt{11}}+1\)
Bài 1 : Tính
a) \(\sqrt{16-2\sqrt{55}}\)
b) \(\sqrt{16-8\sqrt{3}}\)
c) \(\sqrt{17+12\sqrt{5}}\)
d) \(\sqrt{35+12\sqrt{6}}\)
e)\(\sqrt{29-12\sqrt{5}}\)
f) \(\sqrt{2-\sqrt{3}}\)
g) \(\sqrt{7-\sqrt{33}}\)
Tính
1, \(\sqrt{3+2\sqrt{2}}\) 7, \(\sqrt{10-2\sqrt{21}}\)
2, \(\sqrt{4-2\sqrt{3}}\) 8, \(\sqrt{11+2\sqrt{18}}\)
3, \(\sqrt{5+2\sqrt{6}}\) 9, \(\sqrt{14-2\sqrt{33}}\)
4, \(\sqrt{7-2\sqrt{10}}\)
5, \(\sqrt{15-6\sqrt{6}}\)
6, \(\sqrt{8+2\sqrt{15}}\)
các bạn ơi ! giúp mik với đi
Rút gọn biểu thức sau:
1) \(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)
2) \(\dfrac{\sqrt{2}-1}{\sqrt{2}+2}-\dfrac{1}{1+\sqrt{2}}+\dfrac{\sqrt{2}+1}{\sqrt{2}}\)
