\(=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{4-\left(2+\sqrt{2+\sqrt{3}}\right)}\)
\(=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2-\sqrt{2+\sqrt{3}}}\)
\(=\sqrt{2+\sqrt{3}}.\sqrt{4-\left(2+\sqrt{3}\right)}\)
\(=\sqrt{2+\sqrt{3}}.\sqrt{2-\sqrt{3}}\)
\(=\sqrt{4-3}=1\)
ai làm giúp với chịu rồi
\(\sqrt{4\cdot\sqrt{2}+4\cdot\sqrt{10-8\cdot\sqrt{3-2\cdot\sqrt{2}}}}\)
bài 1: tính
a) \(\sqrt{1,2\cdot27}\) b) \(\sqrt{55\cdot77\cdot35}\)
c) (\(\sqrt{3}-\sqrt{2}\) )\(^2\) d) (3\(\sqrt{2}-1\))*(3\(\sqrt{2}+1\))
e) (\(\sqrt{6}+7\)) (\(\sqrt{3}-\sqrt{2}\)) i) \(\sqrt{\dfrac{1}{8}}\cdot\sqrt{2}\cdot\sqrt{125}\cdot\sqrt{\dfrac{1}{5}}\)
h) \(\sqrt{\sqrt{2}-1}\cdot\sqrt{\sqrt{2}}+1\)
bài 2: tính
a) \(\sqrt{9}-\sqrt{17}\cdot\sqrt{9}+\sqrt{17}\)
b) 2\(\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)
c) \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\) d) \(\dfrac{\sqrt{10}+\sqrt{15}}{\sqrt{8}+\sqrt{12}}\)
e) \(\dfrac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}\) f) \(\dfrac{x+\sqrt{xy}}{9+\sqrt{xy}}\) (xy>0)
Tính:
a) \(\left(\sqrt{7}-\sqrt{5}+\sqrt{2}\right)\)\(\left(\sqrt{2}-\sqrt{7}-\sqrt{5}\right)\)
b) \(\sqrt{2}\cdot\sqrt{2+\sqrt{3}}\)
c) \(\left(\sqrt{2}-\sqrt{6}\right)\)\(\sqrt{2+\sqrt{3}}\)
Thực hiện phép tính:
a) \(\left(\sqrt{ab}+2\sqrt{\dfrac{b}{a}}-\sqrt{\dfrac{a}{b}+\sqrt{\dfrac{1}{ab}}}\right)\cdot\sqrt{ab}\)
b) \(\left(\dfrac{am}{b}\sqrt{\dfrac{n}{m}}-\dfrac{ab}{n}\sqrt{mn}+\dfrac{a^2}{b^2}\sqrt{\dfrac{m}{n}}\right)\cdot a^2b^2\cdot\sqrt{\dfrac{n}{m}}\)
1/ so sánh
a, \(3+\sqrt{5}\) và \(2\sqrt{2}+\sqrt{6}\)
b, \(2\sqrt{3}+4\) và \(3\sqrt{2}+\sqrt{10}\)
c, \(18\) và \(\sqrt{15}\cdot\sqrt{17}\)
d, \(\sqrt{27}+\sqrt{26}+1\) và \(\sqrt{48}\)
tính: \(\dfrac{\sqrt{18}}{\sqrt{2}}\cdot\sqrt{2}\)
RÚT GỌN
\(\sqrt{x-\sqrt{x^2-1}}\cdot\sqrt{x+\sqrt{x^2-1}}\)
Chứng minh
a)\(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}=8\)
b)(\(\dfrac{1}{5-2\sqrt{6}}+\dfrac{2}{5+2\sqrt{6}}\)
tính: \((\dfrac{\sqrt{4}}{3}-\sqrt{3}+\dfrac{\sqrt{25}}{3})\cdot\sqrt{12}\)