\(=\sqrt{17-4\sqrt{\left(\sqrt{5}+2\right)^2}}=\sqrt{17-4\left(\sqrt{5}+2\right)}\)
\(=\sqrt{9-4\sqrt{5}}=\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}-2\)
Tính :
a. \(\sqrt{\left(\sqrt{3}-3\right)^2}-\sqrt{16+6\sqrt{3}}\)
b. \(\dfrac{3}{\sqrt{5}-\sqrt{2}}+\dfrac{2}{2+\sqrt{2}}+\dfrac{\sqrt{5}-5}{\sqrt{5}-1}\)
c. \(2+\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
d. \(\left(\sqrt{5-2\sqrt{6}+\sqrt{2}}\right).\dfrac{1}{\sqrt{3}}\)
tính
1.\(\sqrt{147}+\sqrt{54}-4\sqrt{27}\)
2.\(\sqrt{28}-4\sqrt{63}+7\sqrt{112}\)
3.\(\sqrt{49}-5\sqrt{28}+\dfrac{1}{2}\sqrt{63}\)
4.\(\left(2\sqrt{6}-4\sqrt{3}-\dfrac{1}{4}\sqrt{8}\right).3\sqrt{6}\)
5.(\(2\sqrt{1\dfrac{9}{16}}-5\sqrt{5\dfrac{1}{16}}\)):\(\sqrt{16}\)
6.\(\left(\sqrt{48}-3\sqrt{27}-\sqrt{147}\right):\sqrt{3}\)
7.\(\left(\sqrt{50}-3\sqrt{49}\right):\sqrt{2}-\sqrt{162}:\sqrt{2}\)
8.\(\left(2\sqrt{1\dfrac{9}{10}}-\sqrt{5\dfrac{1}{10}}\right):\sqrt{10}\)
9.\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
10.\(2\sqrt{27}-6\sqrt{\dfrac{4}{3}}+\dfrac{3}{5}\sqrt{75}\)
11.\(\dfrac{\sqrt{18}}{\sqrt{2}}-\dfrac{\sqrt{12}}{\sqrt{3}}\)
12.\(\dfrac{\sqrt{27}}{\sqrt{3}}+\dfrac{\sqrt{98}}{\sqrt{2}}-\sqrt{175}:\sqrt{7}\)
13.\(\left(\dfrac{\sqrt{8}}{\sqrt{2}}-\dfrac{\sqrt{180}}{\sqrt{5}}\right).\sqrt{5}-\sqrt{\dfrac{81}{11}}.\sqrt{11}\)
14.\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
15.\(\left(3\sqrt{2}-2\sqrt{3}\right)\left(3\sqrt{2}+2\sqrt{3}\right)\)
16.\(\left(1+\sqrt{5}-\sqrt{3}\right)\left(1+\sqrt{5}+\sqrt{3}\right)\)
RÚT GỌN
a.\(\dfrac{1}{\sqrt{x+2\sqrt{x-1}}}+\dfrac{1}{\sqrt{x-2\sqrt{x-1}}}\)
b. \(\dfrac{1}{2\sqrt{3}+\sqrt{9+4\sqrt{5}}}-\dfrac{1}{2\sqrt{3}-\sqrt{9-4\sqrt{5}}}\)
bài 3 : rút gọn P = \(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-\dfrac{1}{\sqrt{4}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{9}}\)
Tính các biểu thức sau:
a)\(\sqrt{3+2\sqrt{2}}-\sqrt{17-12\sqrt{2}}\)
b)\(\sqrt{5-2\sqrt{6}}-\sqrt{14-4\sqrt{6}}-\sqrt{48}\)
c)\(\sqrt{11+3\sqrt{8}}-\sqrt{17-12\sqrt{2}}-4\sqrt{8}\)
Mọi người ơi,em đang bí những bài này,nếu ai biết thì giải giúp em nhé!
Em xin cảm ơn ạ!!!
1 giải phương trình
x - 7\(\sqrt{x-3}\) + 9 = 0
2 chỉ ra chỗ sai trong các biến đổi sau
x\(\sqrt[]{\dfrac{2}{5}}\) = \(\sqrt[]{\dfrac{2x^2}{5}}\)
ab\(\sqrt[]{\dfrac{a}{b}}\)= a\(\sqrt{\dfrac{ab^2}{b}^{ }}\)= a\(\sqrt{ab}\)
3 chứng minh giá trị các biểu thức sau là nguyên
A = \(\sqrt{3-2\sqrt{2}}\) - \(\sqrt{3+3\sqrt{2}}\)
B = 2\(\sqrt{9-4\sqrt{5}}\) - \(\sqrt{21-4\sqrt{5}}\)
4 rút gọn biểu thức sau
a,\(\dfrac{10}{9}\)*(\(\sqrt{0,8}+\sqrt{1,25}\) )
b,4\(\sqrt{\dfrac{2}{9}}+\sqrt{2}+\sqrt{\dfrac{1}{18}}\)
c,\(\dfrac{1}{\sqrt{5}-1}-\dfrac{1}{\sqrt{5}+1}\)
d, 6\(\sqrt{a}+\dfrac{2}{3}\sqrt{\dfrac{a}{4}}-a\sqrt{\dfrac{9}{a}}+\sqrt{7}\)
e, \(11\sqrt{5a}-\sqrt{125a}+\sqrt{20a}-4\sqrt{45a}+9\sqrt{a}\)
f, \(5a\sqrt{25ab^3}-\sqrt{3}\sqrt{12a^3b^3}+9ab\sqrt{9ab}-5b\sqrt{81a^3b}\)
g, \(\sqrt{\dfrac{a}{b}}+\sqrt{ab}-\dfrac{a}{b}\sqrt{\dfrac{b}{a}}\)
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=(\(\left(\sqrt{3}-1\right).\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
1)Rút gọn biểu thức:
a) \(\dfrac{10}{9}\left(\sqrt{0,8}+\sqrt{ }1,25\right)\)
b) \(4\sqrt{\dfrac{2}{9}}+\sqrt{2}+\sqrt{\dfrac{1}{18}}\)
c) \(\dfrac{1}{\sqrt{5}-1}-\dfrac{1}{\sqrt{5}+1}\)
d) \(6\sqrt{a}+\dfrac{2}{3}\sqrt{\dfrac{a}{4}}-a\sqrt{\dfrac{9}{a}}+7\) với a >0
1. Trục căn thức ở mẫu:
a) \(\dfrac{1}{1+\sqrt{2}+\sqrt{5}} \)
b) \(\dfrac{1}{\sqrt{x}+\sqrt{x+1}}\)
2. Tính:
a) \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-6\sqrt{20}}}}\)
b) \(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
c) \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
3. Cho a = \(\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\)
Chứng minh rằng a là số tự nhiên.
4. Cho b = \(\dfrac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
b có phải là số tự nhiên không?
