a. \(\sqrt{\frac{3}{7}}=\sqrt{\frac{3\cdot7}{7^2}}=\frac{\sqrt{21}}{7}\)

b.\(\sqrt{\frac{7}{20}}=\sqrt{\frac{7\cdot5}{4\cdot5\cdot5}}=\frac{\sqrt{35}}{2\cdot5}=\frac{\sqrt{35}}{10}\)

c.\(\sqrt{\frac{11}{12}}=\sqrt{\frac{11\cdot3}{4\cdot3\cdot3}}=\frac{\sqrt{33}}{2\cdot3}=\frac{\sqrt{33}}{6}\)

d.\(\sqrt{\frac{\left(\sqrt{3}-\sqrt{2}\right)^2}{3}}=\sqrt{\frac{3\left(\sqrt{3}-\sqrt{2}\right)^2}{3\cdot3}}=\frac{\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}{3}=\frac{3-2\sqrt{3}}{3}\)

Mỗi giờ An đi được là:

       1 : 4 = \(\frac{1}{4}\)(quãng đường)

Mỗi giờ Bình đi được là:

       1 : 6 = \(\frac{1}{6}\) (quãng đường)

Mỗi giờ cả hai bạn đi được là:

      \(\frac{1}{4}+\frac{1}{6}=\frac{5}{12}\)(quãng đường)

Thời gian cả hai người đi hết quãng đường AB là:

      1 : \(\frac{5}{12}\)= \(\frac{12}{5}\)(giờ) = 2 giờ 24 phút

Hai người gặp nhau lúc:

         7 giờ + 2 giờ 24 phút = 9 giờ 24 phút

              Đáp số: 9 giờ 24 phút

10*10=100

a)

\(A=\left(\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}+\frac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\\ =\frac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\frac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}\\ =\frac{\sqrt{a}-1}{\sqrt{a}}\)

b) Ta có: \(A=\frac{\sqrt{a}-1}{\sqrt{a}}=\frac{\sqrt{a}}{\sqrt{a}}-\frac{1}{\sqrt{a}}=1-\frac{1}{\sqrt{a}}\)

Với mọi a>0 và a≠1 ta có \(\sqrt{a}>0\Leftrightarrow\frac{1}{\sqrt{a}}>0\)

\(\Rightarrow A=1-\frac{1}{\sqrt{a}}< 1\left(đpcm\right)\)

c)

\(A=1-\frac{1}{\sqrt{a}}=\frac{1}{2}\Leftrightarrow\frac{1}{\sqrt{a}}=\frac{1}{2}\Leftrightarrow\sqrt{a}=2\Leftrightarrow a=4\left(tm\right)\)

Vậy.......

không được ghi những thông tin không liên quan tới toán

đáp số : 12 

nối hai câu đơn đã cho thành 1 câu ghép,sử dụng liên từ thích hợp

1)Jim was absent from class yesterday.he was suffering from a bad cold

=> Jim was absent from class yesterday because he was suffering from a bad cold.

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=> They decided to move their house so (so that) they don't have to travel a long distance to work

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=>Mary hurt her fingers yesterday while(when) she was preparing dinner

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=> At 4pm yesterday, my mother was cleaning the house while I was looking after my younger brother.

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=> They decided to go an excursion since/because they want to get away from work stress.

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=> I didn't know how to use the computer until my father taught me how to use it

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=> I will call you as soon as I arrive at the station.

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=> Mr.peter was walking home when he was robbed of his wallet.

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