tính
1\(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
2\(\left(2\sqrt{3}-3\right):5\sqrt{3}\)
3\(\left(2\sqrt{18}-3\sqrt{8}+6\right):\sqrt{2}\)
4\(\sqrt{27\left(1-\sqrt{3}\right)^2}:3\sqrt{15}\)
5\(\dfrac{a-\sqrt{b}}{\sqrt{b}}:\dfrac{\sqrt{b}}{a+\sqrt{b}}\)
Bài 1:Tính GT các biểu thức:
A= \(\left(\sqrt{5}+\sqrt{3}\right)^2\) - \(\left(\sqrt{5}-\sqrt{8}\right)^2\)
B= \(\sqrt{50}-3\sqrt{98}+2\sqrt{8}-3\sqrt{32}-5\sqrt{18}\)
C= \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
(mink đag cần gấp)
. Làm tính nhân :
a) \(\left(\sqrt{12}-3\sqrt{75}\right).\sqrt{3}\)
b) \(\left(\sqrt{18}-4\sqrt{72}\right).2\sqrt{2}\)
c) \(\left(\sqrt{6}-2\right)\left(\sqrt{6}+7\right)\)
d) \(\left(\sqrt{3}+2\right)\left(\sqrt{3}-5\right)\)
2 . Thực hiện phép tính :
a) \(\left(\sqrt{48}-\sqrt{27}+4\sqrt{12}\right):\sqrt{3}\)
b) \(\left(\sqrt{20}-3\sqrt{45}+6\sqrt{180}\right):\sqrt{5}\)
c) \(\left(2\sqrt{20}-3\sqrt{45}+4\sqrt{80}\right):\sqrt{5}\)
d) \(\left(3\sqrt{24}+4\sqrt{54}-5\sqrt{96}\right):\sqrt{6}\)
e) \(\left(\sqrt{x^2y}-\sqrt{xy^2}\right):\sqrt{xy}\)
f) \(\left(\sqrt{a^3b}+\sqrt{ab^3}-ab\right):\sqrt{ab}\)
g) \(\left(3\sqrt{x^2y}-4\sqrt{xy^2}+5xy\right):\sqrt{xy}\)
h) \(\left(\sqrt{a^3b}+\sqrt{ab^3}-3\sqrt{ab}\right):\sqrt{ab}\)
1. Áp dụng quy tắc khai phương 1 thương, tính:
\(\frac{3\sqrt{128}}{\sqrt{2}}\)
2. Tính:
a. \(\left(\sqrt{32}-\sqrt{50}+\sqrt{8}\right):\sqrt{2}\)
b. \(\left(5\sqrt{48}-3\sqrt{27}+2\sqrt{12}\right):\sqrt{3}\)
c. \(\left(\sqrt{6}-\sqrt{2}\right)\sqrt{2+\sqrt{3}}\)
f. \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
bài 1 rút gọn
a \(A=\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
b\(B=\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
c\(C=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\) d\(D=\sqrt{2+\sqrt{3}}+\sqrt{14-5\sqrt{3}}+\sqrt{2}\)
Tính:
A=\(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
B=\(\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
C=\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
D=\(\sqrt{5\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
E=\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)(2 cách)
F=\(\dfrac{\sqrt{17-12\sqrt{2}}}{\sqrt{3-2\sqrt{2}}}-\dfrac{\sqrt{17}+12\sqrt{2}}{\sqrt{3+2\sqrt{2}}}\)
\(C=\left(2-\sqrt{3}\right)\sqrt{26+15\sqrt{3}}-\left(2+\sqrt{3}\right)\sqrt{26-15\sqrt{3}}\)
D= \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
Rút gọn các biểu thức
A= \(\sqrt{\left(\sqrt{2}-1\right)^2}\)-\(\sqrt{3+2\sqrt{2}}\)
B= \(\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
C= \(\sqrt{\left(2\sqrt{5}-7\right)^2}\)-\(\sqrt{45-20\sqrt{5}}\)
D= \(\sqrt{\left(3-\sqrt{5}\right)^2}\)+\(\sqrt{5}\)
1
a. \(\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\) b.\(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\) c. \(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\)
d. \(\frac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\) e. \(\frac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\) f. \(\frac{\left(\sqrt{5}+2\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)