a. \(\sqrt{48}-2\sqrt{32}-\sqrt{75}+3\sqrt{50}\) = \(4\sqrt{3}-2.4\sqrt{2}-5\sqrt{3}+3.5\sqrt{2}\)

= \(4\sqrt{3}-8\sqrt{2}-5\sqrt{3}+15\sqrt{2}\)  = \(-\sqrt{3}+7\sqrt{2}\)

b. \(\sqrt{20}-15\sqrt{\dfrac{1}{5}}+\sqrt{\left(1-\sqrt{5}\right)^2}\) = \(2\sqrt{5}-3.5.\sqrt{\dfrac{1}{5}}+\left|1-\sqrt{5}\right|\)

= \(2\sqrt{5}-3\sqrt{25.\dfrac{1}{5}}+\sqrt{5}-1\) =  \(2\sqrt{5}-3\sqrt{5}+\sqrt{5}-1\) = \(-1\)

c. \(\dfrac{3}{3+2\sqrt{3}}+\dfrac{3}{3-2\sqrt{3}}\) = \(\dfrac{3\left(3-2\sqrt{3}\right)+3\left(3+2\sqrt{3}\right)}{\left(3+2\sqrt{3}\right)\left(3-2\sqrt{3}\right)}\) 

= \(\dfrac{9-6\sqrt{3}+9+6\sqrt{3}}{\left(3+2\sqrt{3}\right)\left(3-2\sqrt{3}\right)}\) = \(\dfrac{18}{9-12}=\dfrac{18}{-3}=-6\)

33. That restaurant is so dirty that on one wants to eat there.

- It is such a dirty restaurant that no one wants to eat there.

34. “Don’t forget to phone me when you come, Tim” , said Jane.

- Jane told Tim not to forget to phone her when he came.

35. If he doesn’t study harder, he won’t pass the entrance exam.

- Unless he study harder, he won’t pass the entrance exam.

36. You should do your chores before Mom gets home.

- Your chores should be done before Mom gets home.

_{33. “Don’t go out alone when it gets dark, Mary” said Mr Parker.}

_{=> Mr Parker asked Mary not to go out alone when it gets dark.}

_{34. They started working in this factory 10 years ago.}

_{=> They have worked in this factory for 10 years.}

_{35. They worked very hard in spite of their old age.}

_{=> Although they were old, they worked very hard.}

_{36. Peter drives more carefully than John.}

_{=> John doesn't drive as carefully as Peter.}

1. They stole my motorbike last night.

=> My motorbike was stolen last night.

2. She is making a cake.

=> A cake is being made by her.

3. My mother is washing apples in the yard.

=> Apples are being washed in the yard by my mother.

4. I planted a flower plant in the garden.

=> A flower was planted in the garden by me.

5. Someone stole my motorbike last night.

=> My motorbike was stolen last night.

6. My father waters this flower every morning.

=> This flower is watered by my father every morning.

7. John invited Fiona to his birthday party last night.

=> Fiona was invented to John's birthday party last month.

8. Her mother is preparing the dinner in the kitchen.

=> The dinner is being prepared (by her mother) in the kitchen.

9. They sell bread on the street yesterday.

=> Bread was sold on the street (by them) yesterday.

10. Nobody visited Hoa for a long time.

=> Hoa wasn’t visited for a long time.

a) P = \(\dfrac{\sqrt{a}+2}{\sqrt{a}+3}-\dfrac{5}{a+\sqrt{a}-6}+\dfrac{1}{2-\sqrt{a}}\left(ĐKXĐ:a\ge0;a\ne4\right)\)

P = \(\dfrac{\sqrt{a}+2}{\sqrt{a}+3}-\dfrac{5}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+3\right)}-\dfrac{1}{\sqrt{a}-2}\)

P = \(\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)-5-\left(\sqrt{a}+3\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+3\right)}\)

P = \(\dfrac{a-4-5-\sqrt{a}-3}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+3\right)}=\dfrac{a-\sqrt{a}-12}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+3\right)}\)

P  = \(\dfrac{\left(\sqrt{a}-4\right)\left(\sqrt{a}+3\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+3\right)}\)

P = \(\dfrac{\sqrt{a}-4}{\sqrt{a}-2}\) 

b) Ta có: P = \(\dfrac{\sqrt{a}-4}{\sqrt{a}-2}\) = 1 - \(\dfrac{2}{\sqrt{a}-2}\)

Để \(P\in Z\) <=> 1 - \(\dfrac{2}{\sqrt{a}-2}\) \(\in Z\) <=> \(\sqrt{a}-2\inƯ\left(2\right)=\left\{1;-1;2;-2\right\}\)

Ta có bảng sau: 

Vậy để \(P\in Z\) thì  \(a\in\left\{0;1;9;16\right\}\)