Lời giải:
\((\sqrt{28}-2\sqrt{14}+\sqrt{7})\sqrt{7}+7\sqrt{8}\)
\(=(2\sqrt{7}-2\sqrt{2}.\sqrt{7}+\sqrt{7})\sqrt{7}+14\sqrt{2}\)
\(=\sqrt{7}(2-2\sqrt{2}+1).\sqrt{7}+14\sqrt{2}\)
\(=7(3-2\sqrt{2})+14\sqrt{2}=21-14\sqrt{2}+14\sqrt{2}=21\)
rút gọn:
\(A=\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)\)
rút gọn các biểu thức sau
a.A=\(\dfrac{4}{3+\sqrt{7}}+\sqrt{28}\)
b.B=\(\left(\dfrac{\sqrt{x}-1}{x-2\sqrt{x}+1}-\dfrac{2}{\sqrt{x}}\right):\dfrac{2-\sqrt{x}}{x-1}\) (với x>0; x\(\ne\)1; x\(\ne4\))
rút gọn
a) \(\frac{7\sqrt{2}+2\sqrt{7}}{\sqrt{14}}-\frac{5}{\sqrt{7}+\sqrt{5}}\)
b) \(\frac{\sqrt{2}\left(3+\sqrt{5}\right)}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{\sqrt{2}\left(3-\sqrt{5}\right)}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
c) \(\sqrt[3]{16-8\sqrt{5}}+\sqrt[3]{16\text{ }+8\sqrt{5}}\)
helppp mee
Rút gọn biểu thức sau:
\(\sqrt{\left(\sqrt{18}+\sqrt{14}\right).\sqrt{8-3\sqrt{7}}}\)
Rút Gọn Biểu Thức
D=\(\left(\sqrt{14}-\sqrt{6}\right)\left(5+\sqrt{21}\right)\sqrt{5-\sqrt{7}}\)
\(\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\sqrt{4+\sqrt{7}}\)
Rút gọn các biểu thức:
\(a,\sqrt{\sqrt{3}+2}\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\)
\(b,\frac{\sqrt{\sqrt{7}-\sqrt{3}}-\sqrt{\sqrt{7}+\sqrt{3}}}{\sqrt{\sqrt{7}-2}}\)
Thực hiện phép tính:
a)\(\frac{5}{a-\sqrt{11}}+\frac{1}{3\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)
b)\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
c)\(\left(\frac{9-2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2-\left(\frac{9+2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2\)
Cho biểu thức A=\(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right):\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
Rút gọn A?
b, Tính A biết x=\(\frac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}+\sqrt{83-18\sqrt{2}}\)
