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Hello,

1. I am not sure whether you would climb such a tall tree.

What is the meaning of "would" here?

2. As far I know, the theatre would be at the end of the street.

What is the meaning of "would" here?

3.Don't you wish that the fairy should/would grant you a wish.

Which one is correct "should/would"?

4.I guess we should ask the teacher before we leave the room.

What is the meaning of "should" here?
Comments  
Would -implies chances or possibility

Would you like to ……?

Would you mind …….?

Should- implies a sense of duty / obligation.

I should give him a hand with the house cleaning. After all, I share the apartment with him.

I should invite Mary to my house-warming party; even though she is new to our department.
"would" doesn't exactly have a meaning in the way that other words have meanings. It's used with another verb (would go, would climb, would see, etc.). We use it when we want to project a sort of imaginary world in which we test out possibilities.

I'm not sure whether you would climb such a tall tree has two parts.

I'm not sure is the part that is in the real world. I am saying that I am not sure about something. Here and now I am not sure.

you would climb such a tree
is the part that is in a projected world. (That's the part that I am not sure about.) In that imagined world I see you standing before a tree. I am not saying that you will climb the tree. I am not saying that you will not climb the tree. I am imagining a situation in which maybe you will climb the tree and maybe you will not climb the tree. The sentence as a whole is saying that I am not sure which of those two actions you will choose in that imagined world.

Note that would is a little like will and a little unlike will. Suppose I say

I'm not sure whether you will climb such a tall tree.

In this case we are probably both standing before a tall tree. We are in the real world. Both parts of the sentence are in the real world.

Suppose I say

I'm not sure whether you would climb such a tall tree.

In this case we don't have to be standing before a tall tree. The tall tree is just something we are thinking about. We have a picture of the tree in our minds. The second part of the sentence -- the part with would -- is in a sort of imaginary world.

CJ
Students: Are you brave enough to let our tutors analyse your pronunciation?
Goodman
Would -implies chances or possibility

Would you like to ……?

Would you mind …….?

In these sentences-- "Would you like to...?" and "Would you mind.." -- "would" is used to express a polite request or offer.
Hello Goodman,

What should I select for the sentence (3)?
After the verb "wish" we use "would" instead of "will".

The fairy will grant you a wish.
Don't you hope that the fairy will grant you a wish?
Don't you wish that the fairy would grant you a wish?

CJ
Students: We have free audio pronunciation exercises.
"should" is often related to what is advisable.

We should ask the teacher. It is advisable for us to ask the teacher.


In other words,

It would not be a very good idea not to ask the teacher.

CJ
Hi Hanuman,

To me "would" is the right choice. Others are right about the aux. word (such as could, shall etc...) that it's difficult to define them. I was taught that they are conditional words. It depends on the context and tone in which they are used. As to you question, I have no doubt, it's "would".