Question

Why mathematicians use radicals instead of decimals?

For instance: √350 in exact form is: 5√14
, While in decimals its: 18.708

So why not use 18.708 over 5√14 since both will yield the same result?

Answer 1

Mathematicians use radicals instead of decimals to provide a more accurate answer. For example, √14 would be a never ending decimal, but rounded it would be 3.74165738677. So do most imperfect squares such as √2 or √8. To get a more accurate number for an answer, it is better to use radicals as rounded numbers would not get the exact answer.