là dấu cộng chứ không phải dấu nhân hả bn
7\(\sqrt{2}\) +5\(\sqrt{3}\)\(\approx\)18.55974897
Rút gọn
\(A=\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
Rút gọn các biểu thức:
1. \(\sqrt{28}-2\sqrt{252}+3\sqrt{175}+3\sqrt{567}\)
2. \(\sqrt{\left(\sqrt{3}+1\right)^2}+\sqrt{7-4\sqrt{3}}\)
3. \(\sqrt{9-4\sqrt{5}}-\sqrt{\dfrac{8}{7-3\sqrt{5}}}\)
4. \(\dfrac{\sqrt{3}}{2-\sqrt{3}}+\dfrac{2}{2+\sqrt{3}}\)
5. \(\dfrac{2\sqrt{2}+1}{1+\sqrt{2}}+\dfrac{1-2\sqrt{2}}{1-\sqrt{2}}+\left(2-\sqrt{3}\right).\left(2+\sqrt{3}\right)\)
6. \(\sqrt{\dfrac{2}{3-\sqrt{5}}}+\sqrt{\dfrac{2}{7+\sqrt{45}}}\)
7. \(\dfrac{\sqrt{2}}{\sqrt{1+\sqrt{2}}-1}-\dfrac{\sqrt{2}}{\sqrt{1+\sqrt{2}}+1}\)
8. \(\sqrt{6-2\sqrt{5}}+\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}-\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}\)
5 câu:
1) \(\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{6}+2}-\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{6}-2}\)
2) \(\dfrac{3}{\sqrt{5}-\sqrt{2}}-\dfrac{2}{2-\sqrt{2}}+\dfrac{1}{\sqrt{3}+\sqrt{2}}\)
3) \(\dfrac{12}{\sqrt{5}+1}-\dfrac{4}{\sqrt{5}+2}+\dfrac{20}{3+\sqrt{5}}\)
4) \(\dfrac{5}{3-\sqrt{7}}-\dfrac{2}{\sqrt{2}+\sqrt{3}}-\dfrac{1}{\sqrt{2}-1}\)
5) \(\dfrac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\dfrac{3+\sqrt{3}}{\sqrt{3}}-\dfrac{4}{\sqrt{7}-1}\)
A=\(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
B=\(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}-\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
rút gọn biểu thức
Bài : Thu gọn
1) \(\dfrac{3\sqrt{5}-5\sqrt{3}}{\sqrt{15}-3}\)
2) \(\dfrac{\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{3}}\)
3) \(\dfrac{7+4\sqrt{3}}{2+\sqrt{3}}\)
4) \(\dfrac{16-6\sqrt{7}}{\sqrt{7}-3}\)
5) \(\dfrac{\left(\sqrt{3}-\sqrt{2}\right)^2+4\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
6) \(\dfrac{\left(\sqrt{3}+2\sqrt{5}\right)^2-8\sqrt{15}}{\sqrt{6-2\sqrt{10}}}\)
\(5\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\dfrac{5}{2}}\right)^2+\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\dfrac{3}{2}}\right)^2\)
Tính
\(\dfrac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
\(\dfrac{\dfrac{\sqrt{2+\sqrt{3}}}{2}}{\dfrac{\sqrt{2+\sqrt{3}}}{2}-\dfrac{2}{\sqrt{6}}+\dfrac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)
\(\dfrac{1+\dfrac{\sqrt{3}}{2}}{1+\sqrt{1+\dfrac{\sqrt{3}}{2}}}+\dfrac{1-\dfrac{\sqrt{3}}{2}}{1-\sqrt{1-\dfrac{\sqrt{3}}{2}}}\)
A=\(\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}\)
B=\(5\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\dfrac{5}{2}}\right)^2+\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\dfrac{3}{2}}\right)^2\)
Rút gọn các biểu thức sau:
a)\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
b)\(\sqrt{m+2\sqrt{m-1}}+\sqrt{m-2\sqrt{m-1}}\)
c)\(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}\)\(.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\)\(.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)