e ) \(\left(5\sqrt{2}-2\sqrt{5}\right)\left(5\sqrt{2}+2\sqrt{5}\right)=\left(5\sqrt{2}\right)^2-\left(2\sqrt{5}\right)^2\)
\(=50-20=30\)
f ) \(\sqrt{27^2-23^2}=\sqrt{\left(27+23\right)\left(27-23\right)}\)
\(=\sqrt{50.4}=\sqrt{200}=10\sqrt{2}\)
g ) \(\sqrt{37^2-35^2}=\sqrt{\left(37+35\right)\left(37-35\right)}=\sqrt{72.2}=\sqrt{144}=12\)
Rút gọn:
A = \(\sqrt{2}\left(\sqrt{8}-\sqrt{32}-2\sqrt{18}\right)\)
B = \(\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
C = \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
D = \(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}+\sqrt{2}}\)
E = \(\left(\sqrt{2}-\sqrt{3}+\sqrt{5}\right)\sqrt{2}+2\sqrt{5}\)
F = \(\left(\sqrt{14}-\sqrt{10}\right)\left(\sqrt{6+\sqrt{35}}\right)\)
G = \(\sqrt{11-4\sqrt{7}}-\sqrt{2}\times\sqrt{8+3\sqrt{7}}\)
B= \(\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\sqrt{2}\)
C= \(\sqrt{4-\sqrt{7}}-\sqrt{4}+\sqrt{7}\)
D= \(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}+\sqrt{2}}\)
E= \(\sqrt{4+2\sqrt{2}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
F= \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right)\sqrt{2}+2\sqrt{5}\)
G= \(\left(\sqrt{14}-\sqrt{10}\right).\left(\sqrt{6+\sqrt{35}}\right)\)
H= \(\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
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)\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
A)\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
B)\(\left(\sqrt{2}+1^{ }\right)^3-\left(\sqrt{2}-1\right)^3\) C)\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\) D)\(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\) E)\(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\) F)\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
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, \(2\sqrt{3}\left(\sqrt{2}-3\right)+\left(2-\sqrt{3}\right)^2+6\sqrt{3}\)
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!!
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) \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)
1. Tính
a. \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b.\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
c.\(\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
B1: tính : a, \(\sqrt{400.0,81}\)
b, \(\sqrt{\dfrac{5}{27}.\dfrac{3}{20}}\)
c, \(\sqrt{\left(-5\right)^2.3^2}\)
d, \(\sqrt{\left(2-\sqrt{5}\right)^2.\left(2+\sqrt{5}\right)^2}\)