\(M=\sqrt{\dfrac{8^{10}-4^{10}}{4^{11}-8^4}}\)
\(M=\sqrt{\dfrac{\left(2^3\right)^{10}-\left(2^2\right)^{10}}{\left(2^2\right)^{11}-\left(2^3\right)^4}}\)
\(M=\sqrt{\dfrac{2^{30}-2^{20}}{2^{22}-2^{12}}}\)
\(M=\sqrt{\dfrac{2^{20}\left(2^{10}-1\right)}{2^{12}\left(2^{10}-1\right)}}\)
\(M=\sqrt{2^8}=16\)
Không dùng máy tính bỏ túi, tính M = \(\sqrt{\dfrac{8^{10}-4^{10}}{4^{11}-8^4}}\)
Rút gọn :
\(\dfrac{1}{\sqrt{11-2\sqrt{30}}}-\dfrac{3}{\sqrt{7-2\sqrt{10}}}+\dfrac{4}{\sqrt{8+4\sqrt{3}}}\)
\(C=\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
\(B=\dfrac{20}{3+\sqrt{5}+\sqrt{2+2\sqrt{5}}}\)
Tính giá trị các biểu thức:
a.\(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right)\sqrt{3}\)
b.\(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)
c.\(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\sqrt{8}\right)3\sqrt{6}\)
d.\(3\sqrt{15\sqrt{50}}+5\sqrt{24\sqrt{8}}-4\sqrt{12\sqrt{32}}\)
Tìm x:
\(\sqrt{9x+18}-0,5\sqrt{4x+8}-\dfrac{4}{5}\sqrt{25x+50}=-10\)
Thực hiện phép tính:
a)2\(\sqrt{50}\) -3 \(\sqrt{32}\) - \(\sqrt{162}\) + 5\(\sqrt{98}\)
b)\(\sqrt{8+2\sqrt{7}}+\sqrt{11-4\sqrt{7}}\)
c)\(\dfrac{10}{\sqrt{5}}+\dfrac{8}{3+\sqrt{5}}-\dfrac{\sqrt{18}-3\sqrt{5}}{\sqrt{2}-\sqrt{5}}\)
-GIÚP MÌNH VỚI Ạ-
CMR:
\(\dfrac{\sqrt{3}+\sqrt{4}+\sqrt{5}+\sqrt{6}+\sqrt{8}+\sqrt{10}}{\sqrt{3}+\sqrt{4}+\sqrt{5}}=1+\sqrt{2}\)
Tính :
\(\dfrac{1}{8\sqrt{9}+9\sqrt{10}}+\dfrac{1}{9\sqrt{10}+10\sqrt{11}}+.....+\dfrac{1}{223\sqrt{224}+224\sqrt{225}}\)
Rút gọn biểu thức:
a) \(\dfrac{\sqrt{9-2\sqrt{6}}-\sqrt{6}}{\sqrt{3}}\) b)\(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}\)
c) \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\) d) \(\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
e) \(\dfrac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\) f) \(\sqrt{9-\sqrt{5\sqrt{3}+5\sqrt{8+10\sqrt{7-4\sqrt{3}}}}}\)