`@` `\text {Ans}`
`\downarrow`
\(S=\sqrt{0,49}+\sqrt{\dfrac{1}{9}}-\sqrt{\dfrac{25}{4}}\)
`S=0,7 + 1/3 - 5/2`
`S=31/30 - 5/2 = -22/15`
Tính tổng sau: \(S=\dfrac{1}{2+\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{4}}+...+\dfrac{1}{100\sqrt{99}+99\sqrt{100}}\)
Không dùng máy tính bỏ túi hãy so sánh :
A= \(\dfrac{1}{\sqrt{1}}+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{24}}+\dfrac{1}{\sqrt{25}}\)và 5
ĐỀ THI TOÁN 9 TP BIÊN HÒA
1. tính
a,\(\sqrt{\dfrac{1,44}{3,61}}\) ; b, \(\sqrt{\dfrac{0,25}{9}}\) ; c, \(\sqrt{1\dfrac{13}{36}}.\sqrt{3\dfrac{13}{36}}\)
d,\(\sqrt{\dfrac{1}{121}.3\dfrac{6}{25}}\) ; e,\(\sqrt{1\dfrac{13}{36}.2\dfrac{2}{49}.2\dfrac{7}{9}}\) ; g,
2. Tính
a, \(\dfrac{\sqrt{245}}{\sqrt{5}}\) ; b, \(\dfrac{\sqrt{3}}{\sqrt{75}}\) ; c, \(\dfrac{\sqrt{10,8}}{\sqrt{0,3}}\) ; d, \(\dfrac{\sqrt{6,5}}{\sqrt{58,5}}\)
3. Tính.
a, \(\sqrt{\dfrac{61^2-60^2}{81}}\) ; b, \(\sqrt{\dfrac{74^2-24^2}{121}}\)
4. Tìm số x không âm, biết:
a, 9 - 4 \(\sqrt{x}=1\) ; b, \(\sqrt{\dfrac{x}{5}}=4\) c, \(\sqrt{7x}< 9\)
Bài 1: Tính
a) \((\sqrt{3}+2)^\text{2}\)
b) -\((\sqrt{2}-1)^\text{2}\)
Bài 2: Tính
a) \(0,5\sqrt{100} - \sqrt{\dfrac{25}{4}}\)
b) \((\sqrt{1\dfrac{9}{16}}- \sqrt{\dfrac{9}{16}}) : 5\)
Bài 3 : So sánh
a) \(\sqrt{3\sqrt{2}} và \sqrt{2\sqrt{3}}\)
b) \(\dfrac{15 - 2\sqrt{10}}{3} và \sqrt{15}\)
So sánh:
a,\(\dfrac{7}{2}\sqrt{\dfrac{1}{12}}\) và \(\dfrac{9}{4}\sqrt{\dfrac{1}{5}}\)
b, \(\sqrt{\dfrac{4}{27}}\) và\(\sqrt{\dfrac{3}{26}}\)
chứng minh bất đẳng thức:
\(\dfrac{1}{\sqrt{1}+\sqrt{3}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+\dfrac{1}{\sqrt{9}+\sqrt{11}}+...+\dfrac{1}{\sqrt{97}+\sqrt{99}}\)<\(\dfrac{9}{4}\)
So sánh A=\(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+...+\dfrac{1}{\sqrt{120}+\sqrt{121}}\)
với B=\(\dfrac{1}{\sqrt{1}}+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+...+\dfrac{1}{\sqrt{35}}\)
Bài: Rút gọn biểu thức:
a, \(\dfrac{1}{\sqrt{7-\sqrt{24}+1}}-\dfrac{1}{\sqrt{7-\sqrt{24}-1}}\)
b, \(\sqrt{\dfrac{4}{9-4\sqrt{5}}}-\sqrt{\dfrac{4}{9+4\sqrt{5}}}\)
1/Tính
A=\(\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
B=\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
C=\(\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\)
D=\(\dfrac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}\)
2/So sánh
\(\sqrt{2017^2-1}-\sqrt{2016^2-1}\) và \(\dfrac{2.1016}{\sqrt{2017^2-1}+\sqrt{2016^2-1}}\)
