a) \(\sqrt{1\frac{9}{16}\times2\frac{14}{25}}=\sqrt{\frac{25}{16}\times\frac{64}{25}}=\sqrt{4}=2\)
b) \(\sqrt{\frac{25^2-9^2}{68}}=\sqrt{\frac{\left(25-9\right)\left(25+9\right)}{68}}=\sqrt{\frac{16.34}{68}}=\sqrt{8}\)
Rút Gọn
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,\(\left(\sqrt{12}+2\sqrt{27}\right)\frac{\sqrt{3}}{2}-\sqrt{150}\)
d,\(\left(\sqrt{18}+\sqrt{0,5}-3\sqrt{\frac{1}{3}}\right)-\left(\sqrt{\frac{1}{8}-\sqrt{75}}\right)\)
e,\(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\)
f,\(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
g,\(\left(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\right)\sqrt{3}\)
h,\(\left(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\right)\sqrt{\frac{1}{2}}\)
i,\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)
j,\(\left(\sqrt{\frac{1}{7}}-\sqrt{\frac{16}{7}}+7\right):\sqrt{7}\)
Tìm giá trị các biểu thức sau bằng cách biến đổi, rút gọn thích hợp:
a) \(\sqrt{\frac{25}{81}.\frac{16}{49}.\frac{196}{9}}\) b) \(\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{34}{81}}\)
c) \(\frac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}\) d) \(\sqrt{21,6}.\sqrt{810}.\sqrt{11^2-5^2}\)
Rút gọn
1,\(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
2,\(\left(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\right)\sqrt{3}\)
3,\(\left(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\right)\sqrt{\frac{1}{2}}\)
4,\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)
5,\(\left(\sqrt{\frac{1}{7}}-\sqrt{\frac{16}{7}}+\sqrt{7}\right):\sqrt{7}\)
Tính các giá trị biểu thức sau : \(\sqrt{\frac{9}{4}-\sqrt{2}}\) , \(\sqrt{\frac{129}{16}+\sqrt{2}}\), \(\sqrt{\frac{289+4\sqrt{72}}{16}}\), \(\sqrt{2}\sqrt{7-3\sqrt{5}}\),\(\sqrt{\frac{59}{25}+\frac{6}{5}\sqrt{2}}\), \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\), \(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
Chứng minh rằng:
a)\(\left(\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\right)^8>3^6\)
b) \(\sqrt[3]{\sqrt[5]{\frac{32}{5}}-\sqrt[5]{\frac{27}{5}}}=\sqrt[5]{\frac{1}{25}}+\sqrt[5]{\frac{3}{25}}-\sqrt[5]{\frac{9}{25}}\)
Giải các phương trình sau
a) \(25\sqrt{\frac{a-3}{25}}-7\sqrt{\frac{4a-12}{9}}-7\sqrt{a^2-9}+18\sqrt{\frac{9a^2-81}{81}}=0\)
b)\(\sqrt{18x+9}-\sqrt{8x+4}+\frac{1}{3}\sqrt{2x+1}=4\)
2\(2\sqrt{\frac{16}{3}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\)
cmr các đẳng thức :
1/\(\sqrt[3]{2}+\sqrt[3]{20}-\sqrt[3]{25}=3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}\)
2/\(\frac{\sqrt[4]{5}+1}{\sqrt[4]{5}-1}=\sqrt[4]{\frac{3+2\sqrt[4]{5}}{3-2\sqrt[4]{5}}}\)
3/\(\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{\frac{1}{9}}-\sqrt[3]{\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}\)
giúp mik vs mik cần gấp lắm
1) cho 25 số tự nhiên a1;a2;a3;....;a25 thỏa
\(\frac{1}{\sqrt{a1}}+\frac{1}{\sqrt{a2}}+...+\frac{1}{\sqrt{a25}}=9\).CM trong 25 số đó có 2 số bằng nhau
2) cho a,b,c là độ dài 3 cạnh tam giác.CMR \(\sqrt{2}\left(a+b+c\right)\le\sqrt{a^2+b^2}+\sqrt{b^2+c^2}+\sqrt{c^2+a^2}\le3\left(a+b+c\right)\)
3) cho a,b,c >0.CMR \(\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{a+c}}+\sqrt{\frac{c}{a+b}}>2\)
