Question

Which do you prefer: leaving √5 in radical form, or converting it to a decimal? Why? When would it be useful to use each?

Answer 1

Answer:

Leaving as a radical form

Why?

Because that's the whole value if you convert it to a decimal you cannot write all the numbers, and in the radical form it has all the numbers

It would be useful when we are working with equations for example the quadratic equation, if you get that x=√5, you would want the exact value. And there are more useful

Answer 2

Answer:

I prefer leaving the answer as √5 since it is a shorter form and exact form of the answer.

Here are reasons for leaving it as a radical form or a decimal approximation.

If you are looking for an exact answer, then you should leave it as √5. For example, if you are told a square has area 5 square units, then the exact length of the side is √5 units.

If √5 is the length of something that has to be made to that length, then you need an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then you need an approximation of √5 ft, such as 2.24 ft, so you can make each side of the cardboard square in the length of 2.24 ft.