\(\sqrt{49-5\sqrt{96}}-\sqrt{49+5\sqrt{96}}\)
\(=\sqrt{49-20\sqrt{6}}-\sqrt{49+20\sqrt{6}}\)
\(=\sqrt{\left(5-2\sqrt{6}\right)^2}-\sqrt{\left(5+2\sqrt{6}\right)^2}\)
\(=\left(5-2\sqrt{6}\right)-\left(5+2\sqrt{6}\right)\)
\(=-4\sqrt{6}\)
Rút gọn ;
a. \(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}\)
b. ( 3\(\sqrt{2}+\sqrt{10}\) ).\(\sqrt{38-12\sqrt{5}}\)
Giúp mình với!mai nộp r!cảm ơn mn trc nhé!!!!
(các bạn làm đầy đủ bước nhá)
32, \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
33, \(\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)
34, \(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}\)
35,\(\sqrt{31-8\sqrt{15}}+\sqrt{24-6\sqrt{15}}\)
36, \(\sqrt{49-5\sqrt{96}}-\sqrt{49+5\sqrt{96}}\)
37, \(\sqrt{3+2\sqrt{2}}+\sqrt{5-2\sqrt{6}}\)
Tính : \(\sqrt{14-4\sqrt{6}}-\frac{\sqrt{5}+1}{\sqrt{2}}+\sqrt{11+\sqrt{96}}+\sqrt{3-\sqrt{5}}\)
1.Chứng minh
a) \(\sqrt[4]{49+20\sqrt{6}}+\sqrt[4]{49-20\sqrt{6}}=2\sqrt{3}\)
b) A= \(\dfrac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}+\sqrt{2}}\) là số nguyên.
tính:giải chi tiết nha
\(\sqrt{29-4\sqrt{7}}\)
\(\sqrt{19+6\sqrt{2}}\)
\(\sqrt{28-6\sqrt{3}}\)
\(\sqrt{46-6\sqrt{5}}\)
\(\sqrt{49+8\sqrt{3}}\)
\(\sqrt{32-8\sqrt{7}}\)
Giải các phương trình sau:
a. \(\sqrt{25x+75}+2\sqrt{9x+27}=5\sqrt{x+3}+18\)
b. \(\sqrt{4x-8}-14\sqrt{\dfrac{x-2}{49}}=\sqrt{9x-18}+8\)
Rút gọn
\(A=\sqrt{47+\sqrt{5}}.\sqrt{7-\sqrt{2+\sqrt{5}}}.\sqrt{7+\sqrt{2+\sqrt{5}}}\)
\(B=\sqrt{49-20\sqrt{6}}+\sqrt{106+20\sqrt{6}}\)
\(C=\sqrt{302-20\sqrt{6}}+\sqrt{203-20\sqrt{6}}\)
Rút gọn
\(A=\sqrt{47+\sqrt{5}}.\sqrt{7-\sqrt{2+5}}.\sqrt{7-\sqrt{2+5}}\)
\(B=\sqrt{49-20\sqrt{6}}+\sqrt{106+20\sqrt{6}}\)
\(C=\sqrt{302-20\sqrt{6}}+\sqrt{203-20\sqrt{6}}\)
MÌNH CẦN GẤP
Rút gọn biểu thức
\(a.\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
\(b.\sqrt{41-\sqrt{160}}+\sqrt{49+\sqrt{90}}\)
\(c.\dfrac{x-y}{\sqrt{x}-\sqrt{y}}\left(x\ge0;y\ge0;x\ne y\right)\)
\(d.\dfrac{y+1-2\sqrt{y}}{\sqrt{y}-1}\left(y\ge0;y\ne1\right)\)
\(e.\sqrt{x+2+2\sqrt{x+1}}-\sqrt{x+2-2\sqrt{x+1}}\)
