a) \(\sqrt{36-6\times2\sqrt{5}+5-5}\)
=\(\sqrt{\left(6-\sqrt{5}\right)^2-5}\)=\(\sqrt{\left(6-\sqrt{5}-\sqrt{5}\right)\left(6-\sqrt{5}+\sqrt{5}\right)}\)
=\(\sqrt{\left(5-2\sqrt{5}+1\right)\times6}\)
=\(\sqrt{\left(\sqrt{5}-1\right)^2\times6}\)
=(\(\sqrt{5}-1\))\(\times\)\(\sqrt{6}\)
Câu b muộn rùi nghỉ đây bạn tự nghĩ đi dễ mà
Tính thu gọn :
a , \(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
b , \(\sqrt{27+12\sqrt{5}}-\sqrt{27-12\sqrt{5}}\)
c , \(\sqrt{15-6\sqrt{6}}+\sqrt{15+\sqrt{6\sqrt{6}}}\)
d , \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
e , \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
f , \(\sqrt{5+\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
Rút gọn
a) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
b) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
c) \(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
d) \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
e) \(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
Tính giá trị các biểu thức:
a.\(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right)\sqrt{3}\)
b.\(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)
c.\(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\sqrt{8}\right)3\sqrt{6}\)
d.\(3\sqrt{15\sqrt{50}}+5\sqrt{24\sqrt{8}}-4\sqrt{12\sqrt{32}}\)
Tính:
1)a)\(2\sqrt{40.\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{548}\)
b)\(\left(\sqrt{12}+\sqrt{75}+\sqrt{27}\right):\sqrt{15}\)
d)\(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)
e) (\(\sqrt{\dfrac{1}{7}}-\sqrt[]{\dfrac{16}{7}}+\sqrt[]{\dfrac{9}{7}}\)):\(\sqrt{7}\)
2)
a)A=\(\sqrt{3+\sqrt{5+2\sqrt{3}}}.\sqrt{3-\sqrt[]{5+2\sqrt[]{3}}}\)
b) B=\(\sqrt{4+\sqrt{8}}\) . \(\sqrt{2+\sqrt{2+\sqrt{2}}}\) .\(\sqrt{2-\sqrt{2+\sqrt{2}}}\)
1, \(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{10}}\)
2, \(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
3, \(2\sqrt{27}-6\sqrt{\frac{4}{3}}+\frac{3}{5}\sqrt{75}\)
4, \(\sqrt{8\sqrt{3}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}}\)
5, \(\frac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\frac{1}{4}\sqrt{120}-\sqrt{\frac{15}{2}}\)
ai giúp e với ạ
So sánh:
a) \(4\sqrt{7}\) và \(3\sqrt{13}\)
b) \(3\sqrt{12}\) và \(2\sqrt{16}\)
c) \(\dfrac{1}{4}\sqrt{84}\) và \(6\sqrt{\dfrac{1}{7}}\)
d) \(3\sqrt{12}\) và \(2\sqrt{16}\)
e) \(\dfrac{1}{2}\sqrt{\dfrac{17}{2}}\) và \(\dfrac{1}{3}\sqrt{19}\)
Rút gọn:
a) \(\sqrt{24-3\sqrt{15}}-\sqrt{36-9\sqrt{15}}\)
b)\(\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
c)\(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
d) \(\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}\)
e) \(\sqrt{7+\sqrt{13}}-\sqrt{7-\sqrt{13}}\)
f) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
Thực hiện phép tính
a. 2\(\sqrt{\dfrac{16}{3}}\) - 3\(\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
b. \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\)
c.\(2\sqrt{27}-6\sqrt{\dfrac{4}{3}}+\dfrac{3}{5}\sqrt{75}\)
d. \(\dfrac{1}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
e. \(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
d. \(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
e. \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
g. \(\sqrt{4-\sqrt{9}+4\sqrt{2}}\)
Bài 1: Thực hiện phép tính
a/(\(\sqrt{3}-2\sqrt{12}+2\sqrt{4}\))(\(\sqrt{27}+\sqrt{144}-2\sqrt{16}\))
b/(\(2\sqrt{5}+2\sqrt{3}\))2-4\(\sqrt{60}\)
c/\(\sqrt{6}\)(3\(\sqrt{12}-4\sqrt{3}+\sqrt{48}-5\sqrt{6}\))
d/(\(\sqrt{2}-\sqrt{3}\))(\(\sqrt{6}+\sqrt{2}\))(\(\sqrt{2}+\sqrt{3}\))
e/\(\sqrt{10-\sqrt{84}-\sqrt{34+2\sqrt{189}}}\)
f/(\(\frac{2}{\sqrt{3}-1}\)\(+\frac{3}{\sqrt{3}-2}+\frac{15}{3-\sqrt{3}}\))\(\frac{1}{\sqrt{3}+5}\)
