\(A=3\sqrt{2}.\sqrt{6-3\sqrt{3}}+\sqrt{6}.\sqrt{6-3\sqrt{3}}\)
\(A=3\sqrt{\left(3-\sqrt{3}\right)^2}+\sqrt{3}.\sqrt{\left(3-\sqrt{3}\right)^2}\)
\(A=\left(3-\sqrt{3}\right)\left(3+\sqrt{3}\right)\)
\(A=9-3=6\)
Tính
1) \(\sqrt{18}.\sqrt{2}\)
2) \(\sqrt{15^2-9^2}\)
3) \(\sqrt{46-6\sqrt{5}}-\sqrt{46+6\sqrt{5}}\)
4)\(\sqrt{21+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)
5) \(\left(2+\sqrt{5}\right).\sqrt{9-4\sqrt{5}}\)
6)\(\left(3-\sqrt{2}\right).\sqrt{7+4\sqrt{3}}\)
7)\(\left(\sqrt{3}+\sqrt{5}\right).\sqrt{7-2\sqrt{10}}\)
8)\(\left(\sqrt{6}+\sqrt{10}\right).\sqrt{4-\sqrt{15}}\)
9) \(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
10) \(\sqrt{2}\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
11) \(\sqrt{3}-\sqrt{2}-\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
12) \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)
Tính
a) \(\sqrt{\left(4-2\sqrt{3}\right).\left(13+4\sqrt{3}\right)}\)
b) \(\left(\sqrt{3}-2\right).\left(\sqrt{6}+\sqrt{2}\right).\sqrt{\sqrt{3}+2}\)
c)\(\left(3+\sqrt{5}\right).\left(\sqrt{10}-\sqrt{2}\right).\sqrt{3-\sqrt{5}}\)
d) \(\left(4+\sqrt{15}\right).\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
Giúp mk với, mk hứa sẽ tick cho.Cảm ơn nhiều!!
xin các cao nhân giúp đỡ
\(\left(\frac{2\sqrt{2}+3\sqrt{3}}{\sqrt{2}+\sqrt{3}}-\sqrt{6}\right):\left(\sqrt{2}-\sqrt{3}\right)-\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}\)
\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}-\sqrt{12}\right).\left(2+\sqrt{3}\right)\)
\(\sqrt{2}.\sqrt{2-\sqrt{3}}.\left(\sqrt{3}+1\right)\)
\(\sqrt{6+2\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
BT: Tính
a, \(\sqrt{13}.\sqrt{52}\)
b, \(\sqrt{12,5}.\sqrt{0,2}.\sqrt{0,1}\)
c, \(\sqrt{12}-\sqrt{27}+\sqrt{3}\)
d, \(\sqrt{252}-\sqrt{700}+\sqrt{1008}-\sqrt{448}\)
e, \(\left(\sqrt{12}-2\sqrt{75}\right).\sqrt{3}\)
f, \(\sqrt{3}.\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right)\)
g, \(\left(\sqrt{18}+\sqrt{32}-\sqrt{50}\right).\sqrt{2}\)
h, \(\sqrt{50}-\sqrt{18}+\sqrt{200}-\sqrt{162}\)
k, \(\frac{\sqrt{6}+\sqrt{10}}{\sqrt{21}+\sqrt{35}}\)
l, \(\frac{\sqrt{405}+3\sqrt{27}}{3\sqrt{3}+\sqrt{45}}\)
m, \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}-\sqrt{6}-\sqrt{9}-\sqrt{12}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
n, \(\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}\)
p, \(\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)-\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)\)
q, \(2\sqrt{3}\left(\sqrt{2}-3\right)+\left(2-\sqrt{3}\right)^2+6\sqrt{3}\)
Rút gọn biểu thức
a. \(\left(2\sqrt{5}-\sqrt{7}\right)\left(2\sqrt{5}+\sqrt{7}\right)\)
b.\(\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)\)
c. \(\sqrt{9+4\sqrt{5}}\)
d. \(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}\)
e. \(\sqrt{55-6\sqrt{6}}\)
f. \(\sqrt{21-6\sqrt{6}}\)
A)\(\left(3-2\sqrt{2}\right).\left(3+2\sqrt{2}\right)\) B) \(\sqrt{\left(\sqrt{3}-2\right)}^2-\sqrt{\left(\sqrt{3}+2\right)}^2\) C)\(\sqrt{3-2\sqrt[]{2}}-\sqrt{3+2\sqrt{2}}\)
D)\(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+2\right)\)
E) \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\) F)\(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
H)\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
BÀI 1 : THỰC HIỆN PHÉP TÍNH
a, \(\left(1+\sqrt{3}-\sqrt[2]{2}\right)\times\left(1+\sqrt{3}+\sqrt[2]{2}\right)\)
b, \(\left(\dfrac{3}{2}\times\sqrt{6}+2\times\sqrt{\dfrac{2}{3}}-4\times\sqrt{\dfrac{3}{2}}\right)\times\left(3\times\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)
BÀI 2 : rút gọn
B = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-2}}\)
Thực hiện phép tính:
a) ( \(4+\sqrt{15}\))\(\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\)
c) \(\left(\sqrt{3}-\sqrt{2}+1\right)\left(\sqrt{3}-1\right)\)
d) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
