\(A=\sqrt{2}\left(\sqrt{21}+3\right)\sqrt{5-\sqrt{21}}=\left(\sqrt{21}+3\right)\sqrt{10-2\sqrt{21}}=\left(\sqrt{21}+3\right)\left(\sqrt{7}-\sqrt{3}\right)=4\sqrt{3}\)
\(B=\sqrt{2}\left(\sqrt{5}-1\right)\sqrt{3+\sqrt{5}}=\left(\sqrt{5}-1\right)\sqrt{6+2\sqrt{5}}=\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)=5-1=4\)
\(21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{15}\)
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) A = \(21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{15}\)
b) \(B=\dfrac{4+\sqrt{2}-\sqrt{3}-\sqrt{6}+\sqrt{8}}{2+\sqrt{2}-\sqrt{3}}\)
Mọi người giúp với...Please help me!!!!
Rút gọn:
1) \(\dfrac{16-6\sqrt{7}}{\sqrt{7}-3}\)
2) \(\dfrac{\left(\sqrt{3}-\sqrt{2}\right)^2+4\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
3) \(\dfrac{\left(\sqrt{3}+2\sqrt{5}\right)^2-8\sqrt{15}}{\sqrt{6}-2\sqrt{10}}\)
Giúp em với ạ. Help mee !!!
rút gọn biểu thức A=\(\dfrac{\left(2-\sqrt{a}\right)-\left(\sqrt{a+3}\right)}{1+2\sqrt{a}}\) (với a>0) ; B=\(\dfrac{1}{1-\sqrt{2}+\sqrt{3}}-\dfrac{1}{1-\sqrt{2-\sqrt{3}}}\); C=\(\dfrac{1}{\sqrt{5-2}}+\dfrac{1}{\sqrt{5+\sqrt{2}}}\)
a,\(\left(4\sqrt{3}+2\sqrt{5}\right)\sqrt{3}-\sqrt{60}\)
b,\(\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}\)
Tính?
\(\left(\sqrt{21}-7\right)\sqrt{5+\sqrt{21}}\)
J = \(\left(1+\frac{2+\sqrt{2}}{1+\sqrt{2}}\right)\) . \(\left(1-\frac{2-\sqrt{2}}{1-\sqrt{2}}\right)\)
M = \(\frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\frac{1}{\sqrt{6}}\)
N = \(\frac{6}{1+\sqrt{7}}+\frac{1}{\sqrt{7}}\)
O = \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{1}{2-\sqrt{3}}\)
Q = \(\left(\frac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\frac{5}{\sqrt{5}}\right).\left(\sqrt{5}-\sqrt{2}\right)\)
S = \(\frac{2}{\sqrt{5}+1}-\sqrt{\frac{2}{3-\sqrt{5}}}\)
Các thầy cô, các bạn giúp em với ạ. Em cảm ơn !
\(A=\left(5+\frac{7-\sqrt{21}}{\sqrt{7}-\sqrt{3}}\right)\left(\sqrt{16-5\sqrt{7}}\right)\)
rút gọn biểu thức