algebra

Can someone help me with this problem please?

rationalize the denominator and simlify the answer:

5/2 + the square root of 3

Do you mean
5/(2 + sqrt 3) ?
What you wrote could also be interpreted as 2.5 + sqrt 3. You need to be more careful to use parentheses when necessary to avoid confusion.

If you meant 5/(2 + sqrt 3), then multiply numerator and denominator by 2 - sqrt 3.

You will get
5(2 - sqrt3)/(4-3) = 5 (2 - sqrt 3)

There are no parentheses. It looks like this:

5
____
2 + sqrt3

Would the answer then be
10-sqrt3
?

No.
5(2 - sqrt 3) = 10 - 5 sqrt 3

So that is the answer? I forgot to distribute, right?

wouldn't you actually do the 10-5 to get 5, though?

why must you put it in parentheses? why isn't it just 5*2-sqrt3?

While the parentheses are not in the original problem, it's easier if you use them when typing in a problem to make your problem clearer. If you wrote 5 * 2 - sqrt3, by order of operations, you would multiply the 5 and the 2 to get 10, and then subtract sqrt3. Your answer would then be 10-sqrt3, which is incorrect.
By putting in the parentheses to make 5 * (2 - sqrt3), you must distribute to get 10 - 5 * sqrt3, as drwls said.
And you can't do 10 - 5 = 5 here, since the 5 is mutiplied by sqrt3. You would have to subtract the entire unit, 5*sqrt3, from the 10, which can't be done without putting it into a calculator and getting a decimal answer. So the best and most simplified answer here would be the one drwls posted.

Oh, thanks for clearing that for me!

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