\(\sqrt{4+\sqrt{10+2\sqrt{5}}}-\sqrt{4-\sqrt{10+2\sqrt{5}}}\Rightarrow x^2=4+\sqrt{10+2\sqrt{5}}+4-\sqrt{10+2\sqrt{5}}-2\sqrt{\left(4-\sqrt{10+2\sqrt{5}}\right)\left(4+\sqrt{10+2\sqrt{5}}\right)}=8-2\sqrt{6-2\sqrt{5}}=8-2\sqrt{\left(1-\sqrt{5}\right)^2}=8-2\left(\sqrt{5}-1\right)=10-2\sqrt{5}\Rightarrow x=\sqrt{10-2\sqrt{5}}\)
Câu 1: Rút gọn:
a) \(2\sqrt{18}-4\sqrt{50}-3\sqrt{32}\)
b) \(\sqrt{14-6\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
c) \(\dfrac{\sqrt{10}+10}{1+\sqrt{10}}-\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}\)
Câu 2: Giải phương trình:
\(\sqrt{9x^2-30x+25}=5\)
rút gọn A)\(\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5-3}\right)^2}}\)
B) \(\sqrt{6+2\sqrt{5-\sqrt{\left(2\sqrt{3+1}\right)^2}}}\)
C) \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}}}\)
Rút gọn biểu thức :
\((5\sqrt{\dfrac{1}{5}}+\dfrac{1}{2}\sqrt{20}-\dfrac{5}{4}\sqrt{\dfrac{4}{5}+\sqrt{5}}):2\sqrt{5}\) và \(\dfrac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{1\dfrac{1}{3}}\)
Câu 1 :Tính : B = ( 3 - \(\sqrt{5}\)) ( \(\sqrt{5}\) + 3 )
Câu 2 : Rút gọn : \(\dfrac{\sqrt{5}+1}{3-2\sqrt{2}}-\dfrac{\sqrt{10}}{\sqrt{5}-2}+3\left(\sqrt{2}-\sqrt{5}\right)\)
Câu 3: \(\left(\dfrac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}+\dfrac{\sqrt{x}+\sqrt{y}}{1+\sqrt{xy}}\right):\left(1+\dfrac{x+y+2xy}{1-xy}\right)\)
a, Rút gọn biểu thức a
b, Tính giá trị của A khi x + \(\dfrac{2}{2+\sqrt{3}}\)
Rút gọn \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Rút gọn
A= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
B= \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-5}\)
\(\left(\dfrac{\sqrt{6}-\sqrt{10}}{\sqrt{5}-\sqrt{3}}+3\right)\left(3+\dfrac{2\sqrt{5}+\sqrt{6}}{\sqrt{10}+\sqrt{3}}\right)\)
Rút gọn biểu thức trên
1. Rút gọn:
\(A=\sqrt{4+\sqrt{10}+2\sqrt{5}}+\sqrt{4+\sqrt{10}-2\sqrt{5}}\)
Giúp mk vs
rút gọn : 4+ $\sqrt {10 + 2$\sqrt {5} $} $ + $\sqrt {4 -$\sqrt {10 + 2$\sqrt {5} $} $} $