What is the difference between locating 3/5 on a number line and locating √5 on a number line?

3/5 is 0.6 and is a rational number.

√5 however is an irrational number.

It would be quite easy to find 0.6 on a number line. It's only 6/10. It's made up of six tenths.

Now √5 is equal to 2.236067977 to infinitum.

It's made up of many little and random fractions; to a certain degree infinitely many little and random fractions.

This means that you'd never be able to find its precise value on a number line. You could zoom in to that line for eternity and never find the precise value of √5. You'd think you're getting closer to it's precise value - but it slips away and you just can't reach it.

...Welcome to the asymptotic realm of mathematics. You've been pixelated, digitized and spaghettified. Life will never be the same again.

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