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

Respuesta :

mathstudent55

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.

anuksha0456

We shall prefer to keep √5 in radical form, as it is an irrational number and will never give an exact value when converted to decimal form.

What are rational and irrational numbers?

A rational number is any number that can be represented in the form p/q, where p and q are integers, q ≠ 0, and p, q are co-prime to each other, that is, they do not have any common factor except 1.

All terminating and non-terminating recurring decimals are rational numbers.

An irrational number is a real number that cannot be represented in the above form of a rational number.

All non-terminating non-recurring decimals are irrational numbers.

How do we solve the given question?

We are asked, what would we prefer to do. Leave √5 in radical form or convert it into decimal form.

∵ √5 is an irrational number, we will never get a perfect value of it in decimal form, as irrational numbers are non-terminating non-recurring decimals. So, we shall prefer to keep √5 in the radical form.

Use of √5 in radical form: Gives the exact value in our calculations for equations.

Use of √5 = 2.236067977499........... in the decimal form: Used in trigonometry where we need to find the trigonometric ratio.

Learn more about rational and irrational numbers at

https://brainly.com/question/20400557

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