\(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+........+\dfrac{1}{\sqrt{63}+\sqrt{64}}\)
Những câu hỏi liên quan
tính1.sqrt{147}+sqrt{54}-4sqrt{27}2.sqrt{28}-4sqrt{63}+7sqrt{112}3.sqrt{49}-5sqrt{28}+dfrac{1}{2}sqrt{63}4.left(2sqrt{6}-4sqrt{3}-dfrac{1}{4}sqrt{8}right).3sqrt{6}5.(2sqrt{1dfrac{9}{16}}-5sqrt{5dfrac{1}{16}}):sqrt{16}6.left(sqrt{48}-3sqrt{27}-sqrt{147}right):sqrt{3}7.left(sqrt{50}-3sqrt{49}right):sqrt{2}-sqrt{162}:sqrt{2}8.left(2sqrt{1dfrac{9}{10}}-sqrt{5dfrac{1}{10}}right):sqrt{10}9.2sqrt{dfrac{16}{3}}-3sqrt{dfrac{1}{27}}-6sqrt{dfrac{4}{75}}10.2sqrt{27}-6sqrt{dfrac{4}{3}}+dfrac{3}{5}sqrt{75}11....
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tính
1.\(\sqrt{147}+\sqrt{54}-4\sqrt{27}\)
2.\(\sqrt{28}-4\sqrt{63}+7\sqrt{112}\)
3.\(\sqrt{49}-5\sqrt{28}+\dfrac{1}{2}\sqrt{63}\)
4.\(\left(2\sqrt{6}-4\sqrt{3}-\dfrac{1}{4}\sqrt{8}\right).3\sqrt{6}\)
5.(\(2\sqrt{1\dfrac{9}{16}}-5\sqrt{5\dfrac{1}{16}}\)):\(\sqrt{16}\)
6.\(\left(\sqrt{48}-3\sqrt{27}-\sqrt{147}\right):\sqrt{3}\)
7.\(\left(\sqrt{50}-3\sqrt{49}\right):\sqrt{2}-\sqrt{162}:\sqrt{2}\)
8.\(\left(2\sqrt{1\dfrac{9}{10}}-\sqrt{5\dfrac{1}{10}}\right):\sqrt{10}\)
9.\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
10.\(2\sqrt{27}-6\sqrt{\dfrac{4}{3}}+\dfrac{3}{5}\sqrt{75}\)
11.\(\dfrac{\sqrt{18}}{\sqrt{2}}-\dfrac{\sqrt{12}}{\sqrt{3}}\)
12.\(\dfrac{\sqrt{27}}{\sqrt{3}}+\dfrac{\sqrt{98}}{\sqrt{2}}-\sqrt{175}:\sqrt{7}\)
13.\(\left(\dfrac{\sqrt{8}}{\sqrt{2}}-\dfrac{\sqrt{180}}{\sqrt{5}}\right).\sqrt{5}-\sqrt{\dfrac{81}{11}}.\sqrt{11}\)
14.\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
15.\(\left(3\sqrt{2}-2\sqrt{3}\right)\left(3\sqrt{2}+2\sqrt{3}\right)\)
16.\(\left(1+\sqrt{5}-\sqrt{3}\right)\left(1+\sqrt{5}+\sqrt{3}\right)\)
9 tháng 7 2021 lúc 9:39
* Rút gọn biểu thức
a. \(\sqrt{72}-5\sqrt{2}+3\sqrt{12}\)
b. \(6\sqrt{\dfrac{1}{2}}-\dfrac{2}{\sqrt{2}}-5\sqrt{2}\)
c. \(\dfrac{\sqrt{8}-2}{\sqrt{2}-1}+\dfrac{2}{\sqrt{3}-1}-\dfrac{3}{\sqrt{3}}\)
d. \(\sqrt[3]{64}+\sqrt[3]{27}-2\sqrt[3]{-8}\)
\(a.\sqrt{72}-5\sqrt{2}+3\sqrt{12}\\ =6\sqrt{2}-5\sqrt{2}+6\sqrt{3}\\ =\sqrt{2}+6\sqrt{3}\\ b.6\sqrt{\dfrac{1}{2}}-\dfrac{2}{\sqrt{2}}-5\sqrt{2}\\ =3\sqrt{2}-\sqrt{2}-5\sqrt{2}\\ =-3\sqrt{2}\\ c.\dfrac{\sqrt{8}-2}{\sqrt{2}-1}+\dfrac{2}{\sqrt{3}-1}-\dfrac{3}{\sqrt{3}}\\ =2+1+\sqrt{3}-\sqrt{3}\\ =3\\ d.\sqrt[3]{64}+\sqrt[3]{27}-2\sqrt[3]{-8}\\ =4+3+4\\ =11\)
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9 tháng 7 2021 lúc 8:17
* Rút gọn các biểu thức
a. \(\sqrt{72}-5\sqrt{2}+3\sqrt{12}\)
b. \(6\sqrt{\dfrac{1}{2}}-\dfrac{2}{\sqrt{2}}-5\sqrt{2}\)
c. \(\dfrac{\sqrt{8}-2}{\sqrt{2}-1}+\dfrac{2}{\sqrt{3}-1}-\dfrac{3}{\sqrt{3}}\)
d. \(\sqrt[3]{64}+\sqrt[3]{27}-2\sqrt[3]{-8}\)
7 tháng 7 2021 lúc 16:28
* Rút gọn các biểu thức
a. \(\sqrt{72}-5\sqrt{2}+3\sqrt{12}\)
b. \(6\sqrt{\dfrac{1}{2}}-\dfrac{2}{\sqrt{2}}-5\sqrt{2}\)
c. \(\dfrac{\sqrt{8}-2}{\sqrt{2}-1}+\dfrac{2}{\sqrt{3}-1}-\dfrac{3}{\sqrt{3}}\)
d. \(\sqrt[3]{64}+\sqrt[3]{27}-2\sqrt[3]{-8}\)
So sánh:
a) \(-\dfrac{1}{3}\sqrt{63}và-2\sqrt{2}\)
b) \(-2\sqrt{55}và-\dfrac{3}{5}\sqrt{750}\)
c) \(-3\sqrt{7}và-\dfrac{1}{2}\sqrt{260}\)
a) \(\left(-\dfrac{1}{3}\sqrt{63}\right)^2=\dfrac{1}{9}\cdot63=7\)
\(\left(-2\sqrt{2}\right)^2=8\)
mà 7<8
nên \(-\dfrac{1}{3}\sqrt{63}>-2\sqrt{2}\)
b) Ta có: \(\left(2\sqrt{55}\right)^2=4\cdot55=220\)
\(\left(\dfrac{3}{5}\sqrt{750}\right)=\dfrac{9}{25}\cdot750=270\)
mà 220<270
nên \(2\sqrt{55}< \dfrac{3}{5}\sqrt{750}\)
hay \(-2\sqrt{55}< -\dfrac{3}{5}\sqrt{750}\)
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THỰC HIỆN PHÉP TÍNH
1,\(\sqrt{1\dfrac{9}{16}}\)
2,\(\dfrac{\sqrt{12,5}}{0,5}\)
3,\(\sqrt{\dfrac{25}{64}}\)
4,\(\dfrac{\sqrt{230}}{\sqrt{2,3}}\)
5,\((\sqrt{\dfrac{2}{3}}+\sqrt{\dfrac{50}{3}}-\sqrt{24}).\sqrt{6}\)
1) \(\sqrt{1\dfrac{9}{16}}=\sqrt{\dfrac{25}{16}}=\dfrac{5}{4}\)
2) \(\dfrac{\sqrt{12.5}}{0.5}=\sqrt{\dfrac{12.5}{0.25}}=5\sqrt{2}\)
3) \(\sqrt{\dfrac{25}{64}}=\dfrac{5}{8}\)
4) \(\dfrac{\sqrt{230}}{\sqrt{2.3}}=\sqrt{\dfrac{230}{2.3}}=\sqrt{100}=10\)
5) \(\left(\sqrt{\dfrac{2}{3}}+\sqrt{\dfrac{50}{3}}-\sqrt{24}\right)\cdot\sqrt{6}\)
\(=\left(\dfrac{\sqrt{2}}{\sqrt{3}}+\dfrac{5\sqrt{2}}{\sqrt{3}}-2\sqrt{6}\right)\cdot\sqrt{6}\)
\(=\left(\dfrac{6\sqrt{2}}{\sqrt{3}}-2\sqrt{6}\right)\cdot\sqrt{6}\)
\(=0\cdot\sqrt{6}=0\)
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Giải PT:a) dfrac{1}{2}sqrt{x-1}-dfrac{3}{2}sqrt{9x-9}+24sqrt{dfrac{x-1}{64}}-17b) sqrt{18x-9}-0,5sqrt{2x-1}+dfrac{1}{2}sqrt{25left(2x-1right)}+sqrt{49left(2x-1right)}24c) sqrt{36x-72}-15sqrt{dfrac{x-2}{25}}4left(5+sqrt{x-2}right)d) sqrt{dfrac{1}{3x+2}}-dfrac{1}{2}sqrt{dfrac{9}{3x+2}}+sqrt{dfrac{16}{3x+2}}-5sqrt{dfrac{1}{12x+8}}1e) dfrac{1}{2}sqrt{dfrac{49x}{x+2}}-3sqrt{dfrac{x}{4x+8}}-sqrt{dfrac{x}{x+2}}-sqrt{5}0
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Giải PT:
a) \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
b) \(\sqrt{18x-9}-0,5\sqrt{2x-1}+\dfrac{1}{2}\sqrt{25\left(2x-1\right)}+\sqrt{49\left(2x-1\right)}=24\)
c) \(\sqrt{36x-72}-15\sqrt{\dfrac{x-2}{25}}=4\left(5+\sqrt{x-2}\right)\)
d) \(\sqrt{\dfrac{1}{3x+2}}-\dfrac{1}{2}\sqrt{\dfrac{9}{3x+2}}+\sqrt{\dfrac{16}{3x+2}}-5\sqrt{\dfrac{1}{12x+8}}=1\)
e) \(\dfrac{1}{2}\sqrt{\dfrac{49x}{x+2}}-3\sqrt{\dfrac{x}{4x+8}}-\sqrt{\dfrac{x}{x+2}}-\sqrt{5}=0\)
a. ĐKXĐ: $x\geq 1$
PT $\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{3}{2}.\sqrt{9}.\sqrt{x-1}+24.\sqrt{\frac{1}{64}}.\sqrt{x-1}=-17$
$\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17$
$\Leftrightarrow -\sqrt{x-1}=-17$
$\Leftrightarrow \sqrt{x-1}=17$
$\Leftrightarrow x-1=289$
$\Leftrightarrow x=290$
b. ĐKXĐ: $x\geq \frac{1}{2}$
PT $\Leftrightarrow \sqrt{9}.\sqrt{2x-1}-0,5\sqrt{2x-1}+\frac{1}{2}.\sqrt{25}.\sqrt{2x-1}+\sqrt{49}.\sqrt{2x-1}=24$
$\Leftrightarrow 3\sqrt{2x-1}-0,5\sqrt{2x-1}+2,5\sqrt{2x-1}+7\sqrt{2x-1}=24$
$\Leftrightarrow 12\sqrt{2x-1}=24$
$\Leftrihgtarrow \sqrt{2x-1}=2$
$\Leftrightarrow x=2,5$ (tm)
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c. ĐKXĐ: $x\geq 2$
PT $\Leftrightarrow \sqrt{36}.\sqrt{x-2}-15\sqrt{\frac{1}{25}}\sqrt{x-2}=4(5+\sqrt{x-2})$
$\Leftrightarrow 6\sqrt{x-2}-3\sqrt{x-2}=20+4\sqrt{x-2}$
$\Leftrightarrow \sqrt{x-2}=-20< 0$ (vô lý)
Vậy pt vô nghiệm
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d. ĐKXĐ: $x>\frac{-2}{3}$
PT $\Leftrightarrow \sqrt{\frac{1}{3x+2}}-\frac{1}{2}\sqrt{9}.\sqrt{\frac{1}{3x+2}}+\sqrt{16}.\sqrt{\frac{1}{3x+2}}-5\sqrt{\frac{1}{4}}\sqrt{\frac{1}{3x+2}}=1$
$\Leftrightarrow \sqrt{\frac{1}{3x+2}}-\frac{3}{2}\sqrt{\frac{1}{3x+2}}+4\sqrt{\frac{1}{3x+2}}-\frac{5}{2}\sqrt{\frac{1}{3x+2}}=1$
$\Leftrightarrow \sqrt{\frac{1}{3x+2}}=1$
$\Leftrightarrow \frac{1}{3x+2}=1$
$\Leftrightarrow 3x+2=1$
$\Leftrightarrow x=-\frac{1}{3}$
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Không dùng mtct, so sánhA) sqrt{65}+1 và sqrt{63}+1B)dfrac{1}{sqrt{8}}và dfrac{1}{sqrt{7}}C)sqrt{34,9} và 6D) 3sqrt{25,5} và 14E)2sqrt{26}+4 và 13F) sqrt{24}+sqrt{63+3}và 16G) dfrac{46-3sqrt{49}}{4}và sqrt{50}
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Không dùng mtct, so sánh
A) \(\sqrt{65}\)+1 và \(\sqrt{63}\)+1
B)\(\dfrac{1}{\sqrt{8}}\)và \(\dfrac{1}{\sqrt{7}}\)
C)\(\sqrt{34,9}\) và 6
D) \(3\sqrt{25,5}\) và 14
E)\(2\sqrt{26}\)+4 và 13
F) \(\sqrt{24}\)+\(\sqrt{63+3}\)và 16
G) \(\dfrac{46-3\sqrt{49}}{4}\)và \(\sqrt{50}\)
e: \(2\sqrt{26}>9\)
nên \(2\sqrt{26}+4>13\)
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2 . rút gọn biểu thức
a. sqrt{200}-sqrt{32}+sqrt{72}
b. sqrt{175}-sqrt{112}+sqrt{63}
c. dfrac{3}{2}sqrt{6}+2sqrt{dfrac{2}{3}}-4sqrt{dfrac{3}{2}}
d. 4sqrt{20}-3sqrt{125}+5sqrt{45}-15sqrt{dfrac{1}{5}}
e. 5sqrt{dfrac{1}{5}+}dfrac{1}{5}sqrt{20}+sqrt{5}
f. sqrt{dfrac{1}{5}}+sqrt{4,5}+sqrt{12,5}
g. dfrac{1}{2}sqrt{48}-2sqrt{75}-sqrt{54}+5sqrt{1dfrac{1}{3}}
m. 3sqrt{5a}-sqrt{20a}+sqrt{a}+4sqrt{45a}
n. 3sqrt{8}-sqrt{18}-5sqrt{dfrac{1}{2}}+sqrt{50}
i. sqrt{72}+sqrt{4dfrac{1}{2}}-sqrt{32}+sqrt{6...
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2 . rút gọn biểu thức
a. \(\sqrt{200}-\sqrt{32}+\sqrt{72}\)
b. \(\sqrt{175}-\sqrt{112}+\sqrt{63}\)
c. \(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\)
d. \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)
e. \(5\sqrt{\dfrac{1}{5}+}\dfrac{1}{5}\sqrt{20}+\sqrt{5}\)
f. \(\sqrt{\dfrac{1}{5}}+\sqrt{4,5}+\sqrt{12,5}\)
g. \(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\sqrt{54}+5\sqrt{1\dfrac{1}{3}}\)
m. \(3\sqrt{5a}-\sqrt{20a}+\sqrt{a}+4\sqrt{45a}\)
n. \(3\sqrt{8}-\sqrt{18}-5\sqrt{\dfrac{1}{2}}+\sqrt{50}\)
i. \(\sqrt{72}+\sqrt{4\dfrac{1}{2}}-\sqrt{32}+\sqrt{63}-\sqrt{162}\)
a: \(=10\sqrt{2}-4\sqrt{2}+6\sqrt{2}=12\sqrt{2}\)
b: \(=5\sqrt{7}-4\sqrt{7}+3\sqrt{7}=4\sqrt{7}\)
c: \(=\dfrac{3}{2}\sqrt{6}+\dfrac{2}{3}\sqrt{6}-2\sqrt{6}=\dfrac{1}{6}\sqrt{6}\)
d: \(=8\sqrt{5}-15\sqrt{5}+15\sqrt{5}-3\sqrt{5}=5\sqrt{5}\)
e: \(=\sqrt{5}+\dfrac{2}{5}\sqrt{5}+\sqrt{5}=2.4\sqrt{5}\)
f: \(=\dfrac{1}{5}\sqrt{5}+\dfrac{3}{2}\sqrt{2}+\dfrac{5}{2}\sqrt{2}=\dfrac{1}{5}\sqrt{5}+4\sqrt{2}\)
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