In the simplest case, it is use to find the diagonal length of a unit square.
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It can be.
engineering includes using radical functions almost every day
If you work in science or engineering, you will need radical functions (and other advanced math topics) all the time. Otherwise, you won't have much need for radical functions.
Proportions are used in real life to determine prices of things.
No it is not.
Radical expressions are applied in one's daily life. This is used in terms of doing tile work, estimating distances, or designing something that needs measurement.
If by "radical" you mean "square root of", then yes. Both square roots of 25 are real numbers.
Believe it or not, school is a real life situation. If you are using it in school it real life for you.
The diagonal of a unit square, for example, is radical(2).
If you are in school and are studying trig then you are using trig in real life.
Yes.