\(G=\sqrt{\left(2+2\sqrt{3}-\sqrt{2}\right)^2}-\sqrt{\left(2\sqrt{3}-2\right)^2}=\left(2+2\sqrt{3}-\sqrt{2}\right)-\left(2\sqrt{3}-2\right)=4-\sqrt{2}\)
Bài 4: Liên hệ giữa phép chia và phép khai phương
Các câu hỏi tương tự
rút gọn biểu thức sau
a. \(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-4}\)
b. \(\dfrac{a^2\sqrt{b}-\sqrt{ab^3}}{\sqrt{a^3b^2}-b^2}\)
c. \(\dfrac{a^3-2\sqrt{2}}{a-\sqrt{2}}\)
d. \(18-\sqrt{8}+\dfrac{1}{4}\sqrt{2}\)
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\(D=\sqrt{2+\sqrt{3}}+\sqrt{14-5\sqrt{3}}+\sqrt{2}\)
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)
Tính: \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Tính:Asqrt{4+2sqrt{3}}-sqrt{4-2sqrt{3}}Bsqrt{9-4sqrt{5}}+sqrt{9+4sqrt{5}}Csqrt{4-sqrt{7}}-sqrt{4+sqrt{7}}Dsqrt{5sqrt{3+5sqrt{48-10sqrt{7+4sqrt{3}}}}}Eleft(4+sqrt{15}right)left(sqrt{10}-sqrt{6}right)sqrt{4-sqrt{15}}(2 cách)Fdfrac{sqrt{17-12sqrt{2}}}{sqrt{3-2sqrt{2}}}-dfrac{sqrt{17}+12sqrt{2}}{sqrt{3+2sqrt{2}}}
Đọc tiếp
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=\(\dfrac{\sqrt{17-12\sqrt{2}}}{\sqrt{3-2\sqrt{2}}}-\dfrac{\sqrt{17}+12\sqrt{2}}{\sqrt{3+2\sqrt{2}}}\)
. Làm tính nhân :
a) left(sqrt{12}-3sqrt{75}right).sqrt{3}
b) left(sqrt{18}-4sqrt{72}right).2sqrt{2}
c) left(sqrt{6}-2right)left(sqrt{6}+7right)
d) left(sqrt{3}+2right)left(sqrt{3}-5right)
2 . Thực hiện phép tính :
a) left(sqrt{48}-sqrt{27}+4sqrt{12}right):sqrt{3}
b) left(sqrt{20}-3sqrt{45}+6sqrt{180}right):sqrt{5}
c) left(2sqrt{20}-3sqrt{45}+4sqrt{80}right):sqrt{5}
d) left(3sqrt{24}+4sqrt{54}-5sqrt{96}right):sqrt{6}
e) left(sqrt{x^2y}-sqrt{xy^2}right):sqrt{xy}
f) left(sqrt{a^3b}+sqr...
Đọc tiếp
. 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) \(\left(\sqrt{a^3b}+\sqrt{ab^3}-3\sqrt{ab}\right):\sqrt{ab}\)
Rút gọn:
a, sqrt{dfrac{4}{9-4sqrt{5}}} -sqrt{dfrac{4}{9+4sqrt{5}}}
b, dfrac{sqrt{8-4sqrt{3}}}{sqrt{2}}
c, sqrt{14-8sqrt{3}}-sqrt{24-12sqrt{3}}
d, sqrt{2-sqrt{3}}timesleft(sqrt{5}+sqrt{2}right)
Đọc tiếp
Rút gọn:
a, \(\sqrt{\dfrac{4}{9-4\sqrt{5}}}\) -\(\sqrt{\dfrac{4}{9+4\sqrt{5}}}\)
b, \(\dfrac{\sqrt{8-4\sqrt{3}}}{\sqrt{2}}\)
c, \(\sqrt{14-8\sqrt{3}}\)-\(\sqrt{24-12\sqrt{3}}\)
d, \(\sqrt{2-\sqrt{3}}\)\(\times\)\(\left(\sqrt{5}+\sqrt{2}\right)\)
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\(\dfrac{a-\sqrt{b}}{\sqrt{b}}:\dfrac{\sqrt{b}}{a+\sqrt{b}}\)
Giải phương trình sau:
a)sqrt{3}.x-sqrt{12}0
b)sqrt{2}.x+sqrt{2}sqrt{8}+sqrt{18}
c)sqrt{5}.x^2-sqrt{20}0
d)sqrt{x^2+6x+9}3x+6
e)sqrt{x^2-4x+4}-2x+50
f)sqrt{dfrac{2x-3}{x-1}2}
g) dfrac{sqrt{2x-3}}{sqrt{x-1}}2
Đọc tiếp
Giải phương trình sau:
a)\(\sqrt{3}.x-\sqrt{12}=0\)
b)\(\sqrt{2}.x+\sqrt{2}=\sqrt{8}+\sqrt{18}\)
c)\(\sqrt{5}.x^2-\sqrt{20}=0\)
d)\(\sqrt{x^2+6x+9}=3x+6\)
e)\(\sqrt{x^2-4x+4}-2x+5=0\)
f)\(\sqrt{\dfrac{2x-3}{x-1}=2}\)
g) \(\dfrac{\sqrt{2x-3}}{\sqrt{x-1}}=2\\\)