\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2-\sqrt{2+\sqrt{3}}}\)
= \(\sqrt{2+\sqrt{3}}+\sqrt{2^2-\left(\sqrt{2+\sqrt{3}}\right)^2}\)
= \(\sqrt{2+\sqrt{3}}+\sqrt{4-\left(2+\sqrt{3}\right)}\)
= \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
= \(\sqrt{4-3}\)
= \(\sqrt{1}\)
= \(1\)
Tính:
a)\(\sqrt{3\sqrt{2}-2\sqrt{3}}\cdot\sqrt{3\sqrt{2}+2\sqrt{3}}\)
b) \(\sqrt{2+2\sqrt{2-\sqrt{2}}}\cdot\sqrt{2-2\sqrt{2-\sqrt{2}}}\)
c)\(\left(\sqrt{2}-\sqrt{7}\right)\sqrt{9+2\sqrt{14}}\)
So sánh hai số A,B biết \(A=\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2-\sqrt{2+\sqrt{3}}}\)
\(B=\left(\frac{1}{\sqrt{\sqrt{5}+2}}+\sqrt{\sqrt{5}+2}\right)\cdot\frac{1}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
Mình cần gấp nha mng
\(\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-\sqrt{2}\right)\cdot\sqrt{2+\sqrt{3}}\)
Tính: a. \(\left(3\sqrt{2}+\sqrt{6}\right)\cdot\left(6-3\sqrt{3}\right)\)
b. \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
c. \(\left(3-\sqrt{5}\right)\cdot\left(10-\sqrt{2}\right)\cdot\sqrt{3+\sqrt{5}}\)
Giải các phương trình sau:
a)\(\sqrt[3]{9-x}+\sqrt[3]{7+x}=4\)
b)\(\sqrt{x-1}\cdot\sqrt[4]{x^2-4}=\sqrt{x-2}\cdot\sqrt[4]{x^2-1}\)
c)\(\sqrt[4]{9-x^2}+\sqrt{x^2-1}-2\sqrt{2}=\sqrt[6]{x-3}\)
D = \(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)
A = \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
C = \(\dfrac{2\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}\)
F = \(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
B = \(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+...+\dfrac{1}{\sqrt{n-1}+\sqrt{n}}\)
E = \(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-...-\dfrac{1}{\sqrt{24}-\sqrt{25}}\)
\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
\(0.1\cdot\sqrt{\left(-3\right)^2}\cdot\left[6\sqrt{\left(\frac{1}{3}\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\right]^2\)
\(\left(\frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}+2}-\frac{\sqrt{54}}{3}\right)\cdot\frac{2}{\sqrt{6}}\)
\(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right)\div\left(1\div\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
Tính: a. \(\sqrt{2+\sqrt{3}}\cdot\sqrt{2-\sqrt{3}}\)
b. \(\sqrt{\sqrt{10}+1}\cdot\sqrt{\sqrt{10}-1}\)
Chứng minh biểu thức không phụ thuộc vào x
\(K=\sqrt{x}+\dfrac{\sqrt[3]{2-\sqrt{3}}\cdot\sqrt[6]{7+4\sqrt{3}}-x}{\sqrt[4]{9-4\sqrt{5}}\cdot\sqrt{2+\sqrt{5}}+\sqrt{x}}\)
