Thực hiện phép tính: \(\sqrt[3]{2\sqrt{14}-8}.\sqrt[3]{2\sqrt{14}+8}\)
c/ \(\sqrt{\dfrac{2}{8-3\sqrt{7}}}+\dfrac{\sqrt{14}+\sqrt{7}}{\sqrt{2}+1}\)
d/ \(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}-\dfrac{5\sqrt{x}+2}{x-4}\) ( x \(\ge\)0 ; x \(\ne\) 4 )
Rút gọn : \(\left(12-6\sqrt{3}\right)\sqrt{\frac{3}{14-8\sqrt{3}}}-3\sqrt{2\left(1-\sqrt{1-\sqrt{-2\sqrt{3}+4}}\right)+2\sqrt{4+2\sqrt{3}}}\)
Giúp mình vs đúng sẽ tick cho
Tính:
\(A=\left(\sqrt{72}-3\sqrt{24}+5\sqrt{8}\right)\sqrt{2}+4\sqrt{27}\)
\(B=\dfrac{1}{\sqrt{2}-1}+\dfrac{14}{3+\sqrt{2}}\)
\(C=\dfrac{5+3\sqrt{5}}{\sqrt{5}}+\dfrac{3\sqrt{3}}{\sqrt{3}+1}-\left(\sqrt{5}+3\right)\)
\(D=\sqrt{\left(1-\sqrt{2}\right)^2}-3\sqrt{18}+4\sqrt{\dfrac{1}{2}}\)
(\(\frac{3}{\sqrt{2}+1}+\frac{14}{2\sqrt{2}-1}-\frac{4}{2-\sqrt{2}}\))(\(\sqrt{8}+2\))
rút gọn \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\) ; \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Thực hiện phép tính
-\(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
- \(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
-\(\dfrac{\left(5+\sqrt{2}\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
- \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
- \(\dfrac{\sqrt{3}}{1-\sqrt{\sqrt{3}+1}}+\dfrac{\sqrt{3}}{1+\sqrt{\sqrt{3}+1}}\)
1.\(\dfrac{\sqrt{8-4\sqrt{3}}}{\sqrt{\sqrt{6}-\sqrt{2}}}\cdot\sqrt{\sqrt{6}+\sqrt{2}}\)
2.\(\sqrt{16-5\sqrt{7}}\left(5\sqrt{2}+\sqrt{14}\right)+\dfrac{6}{3+\sqrt{10}}\)
Giải phương trình
1.\(\sqrt{2x-3}-\sqrt{5-2x}=3x^2-12x+14\)
2.\(x^2+2x+15=6\sqrt{4x+5}\)
3.\(x^2-5x-8=2\sqrt{x-2}\)
4.\(\sqrt{x+1+\sqrt{x+\frac{3}{4}}}=x+1\)
