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Chứng minh đẳng thức dưới:
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right).\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\) = 1
Làm ơn giúp mình với T^T
Chứng minh đẳng thức dưới bằng 1. Làm ơn giúp tớ với T^T Tớ sẽ tick ngay nha ^^
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right).\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\)
Chứng minh
\(\frac{1}{3\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5\left(\sqrt{3}+\sqrt{2}\right)}+\)+\(\frac{1}{7\left(\sqrt{3}+\sqrt{4}\right)}\)+....+\(\frac{1}{49\left(\sqrt{24}+\sqrt{25}\right)}\)<\(\frac{2}{5}\)
Bài 1. thực hiện phép tínha) sqrt{frac{5+sqrt{21}}{5-sqrt{21}}}+sqrt{frac{5-sqrt{21}}{5+sqrt{21}}} b) sqrt{frac{4+sqrt{7}}{4-sqrt{7}}}+sqrt{frac{4-sqrt{7}}{4+sqrt{7}}}Bài 2. Tính:a) Mleft(2sqrt{2}right)sqrt{2+4sqrt{3+sqrt{2}+sqrt{11-6sqrt{2}}}}b) frac{1}{sqrt{25}+sqrt{24}}+frac{1}{sqrt{24}+sqrt{23}}+...+frac{1}{sqrt{2}+sqrt{1}}4c)frac{left(5sqrt{3}+sqrt{50}right)left(5-sqrt{24}right)}{sqrt{75}0-5sqrt{2}}
Đọc tiếp
Bài 1. thực hiện phép tính
a) \(\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\) b) \(\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}+\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}\)
Bài 2. Tính:a) \(M=\left(2\sqrt{2}\right)\sqrt{2+4\sqrt{3+\sqrt{2}+\sqrt{11-6\sqrt{2}}}}\)
b) \(\frac{1}{\sqrt{25}+\sqrt{24}}+\frac{1}{\sqrt{24}+\sqrt{23}}+...+\frac{1}{\sqrt{2}+\sqrt{1}}=4\)
c)
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}0-5\sqrt{2}}\)
Tính
\(a,\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}\)
\(b,\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}\)
\(c,\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}\)
\(d,\left(\sqrt{6}+2\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(e,\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4\)
Chứng minh bất đẳng thức :
\(\frac{1}{\left(\sqrt{2}+\sqrt{5}\right)^3}+\frac{1}{\left(\sqrt{5}+\sqrt{8}\right)^3}+...+\frac{1}{\left(\sqrt{95}+\sqrt{98}\right)^3}< \frac{1}{19}\)
Bài 7 Thực hiện phép tính a ( frac{sqrt{9}}{2}+frac{sqrt{1}}{2}-sqrt{2} ) sqrt{2}b) left(frac{sqrt{8}}{3}-sqrt{24}+frac{sqrt{50}}{3}right)sqrt{6}c) left(sqrt{6}+sqrt{2}right).left(sqrt{3}-sqrt{2}right)d) left(3sqrt{2}+1right)left(3sqrt{2}-1right)e ) (left(sqrt{5}-2sqrt{3}right)left(sqrt{5}+2sqrt{3}right)g)left(frac{sqrt{2}}{3}-sqrt{frac{3}{2}}right)^2h) sqrt{52}:sqrt{117}i) sqrt{2}:sqrt{72}l ) left(frac{sqrt{1}}{5}-frac{sqrt{9}}{5}right)+sqrt{5}k) left(sqrt{12}+sqrt{27}-sqrt{3}right):sqrt{3}m) ...
Đọc tiếp
Bài 7 Thực hiện phép tính
a ( \(\frac{\sqrt{9}}{2}+\frac{\sqrt{1}}{2}-\sqrt{2}\) ) \(\sqrt{2}\)
b) \(\left(\frac{\sqrt{8}}{3}-\sqrt{24}+\frac{\sqrt{50}}{3}\right)\sqrt{6}\)
c) \(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-\sqrt{2}\right)\)
d) \(\left(3\sqrt{2}+1\right)\left(3\sqrt{2}-1\right)\)
e ) (\(\left(\sqrt{5}-2\sqrt{3}\right)\left(\sqrt{5}+2\sqrt{3}\right)\)
g)\(\left(\frac{\sqrt{2}}{3}-\sqrt{\frac{3}{2}}\right)^2\)
h) \(\sqrt{52}:\sqrt{117}\)
i) \(\sqrt{2}:\sqrt{72}\)
l ) \(\left(\frac{\sqrt{1}}{5}-\frac{\sqrt{9}}{5}\right)+\sqrt{5}\)
k) \(\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right):\sqrt{3}\)
m) \(\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}}\)
n) \(\frac{\sqrt{6-2\sqrt{5}}}{1-\sqrt{5}}\)
Bài 1: Tính
a, \(4\sqrt{8}+\sqrt{18}-6\sqrt{\frac{1}{2}}-\sqrt{200}\)
b, \(\left(\sqrt{27}-2\sqrt{3}+\sqrt{12}\right).\sqrt{3}+\sqrt{75}\)
c,\(\left(\frac{5+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}\right)^2-\left(\frac{5-2\sqrt{6}}{\sqrt{3}-\sqrt{2}}\right)^2\)
d, \(\left(2-\sqrt{2}\right).\left(-5\sqrt{2}\right)-\left(3\sqrt{2}-5\right)^2\)
Chứng minha,sqrt{9-4sqrt{5}}-sqrt{5}-2b,frac{sqrt{2}+1}{sqrt{2}-1}3+2sqrt{2}c,2sqrt{2}left(3-sqrt{2}right)+left(1+2sqrt{2}right)^2-2sqrt{6}9d,sqrt{frac{4}{left(2-sqrt{5}right)^2}}-sqrt{frac{4}{left(2+sqrt{5}right)^2}}8e,left(3+sqrt{5}right)left(sqrt{10}-sqrt{2}right)sqrt{3-sqrt{5}}8f,sqrt{sqrt{2}+1}-sqrt{sqrt{2}-1}sqrt{2left(sqrt{2}-1right)}
Đọc tiếp
Chứng minh
\(a,\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
\(b,\frac{\sqrt{2}+1}{\sqrt{2}-1}=3+2\sqrt{2}\)
\(c,2\sqrt{2}\left(3-\sqrt{2}\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
\(d,\sqrt{\frac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\frac{4}{\left(2+\sqrt{5}\right)^2}}=8\)
\(e,\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3-\sqrt{5}}=8\)
\(f,\sqrt{\sqrt{2}+1}-\sqrt{\sqrt{2}-1}=\sqrt{2\left(\sqrt{2}-1\right)}\)