Difference between Irrational and Preposterous

IRRATIONAL vs PREPOSTEROUS: NOUN

A real number that can not be expressed as the quotient of two integers, an irrational number.
A prime number.
In mathematics, an irrational number, that is, the mark of a cut which separates all rational numbers into two classes, the first having no greatest number, the second no least.
That which is devoid of reason, as one of the lower animals.
An irrational number.

Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.
Being a metric foot containing such a syllable.
Of or relating to an irrational number.
Marked by a lack of accord with reason or sound judgment.
Affected by loss of usual or normal mental clarity; incoherent, as from shock.
Not endowed with reason.
Not consistent with or using reason
Not rational; void of reason or understanding.
Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; -- of assertions and beliefs.
Not capable of being exactly expressed by an integral number, nor by a ratio of integral numbers; surd; -- said especially of roots. See Surd.
Not rational; unfounded or nonsensical.
Of a real number, that cannot be written as the ratio of two integers.
Real but not expressible as the quotient of two integers

Incongruous;inviting ridicule
Absurd, or contrary to common sense.
Contrary to nature or reason; not adapted to the end; utterly and glaringly foolish; unreasonably absurd; perverted.
Having that first which ought to be last; inverted in order.
Completely devoid of wisdom or good sense
Contrary to nature, reason, or common sense; absurd. : foolish.

In algebra, noting a quantity involving a variable raised to a fractional power; or. in a wider sense, noting a quantity not rational, not a sum of products of constants and of variables into one another or into themselves.
In translations of Euclid, and cognate writings, at once incommensurable with the assumed unit and not having its square commensurable with that of the unit. This is the peculiar meaning given by Euclid to α%27λογος, though Plato uses it in sense , above.
In mathematics: In arithmetic, not capable of being exactly expressed by a vulgar fraction, proper or improper; surd.
Without the quality of reason; contrary to reason; illogical; unreasonable: as, irrational motives; an irrational project.
Not rational; without the faculty of reason; void of understanding; unreasoning.
In Greek prosody, incapable of measurement in terms of the fundamental or primary time or metrical unit.

Having that last which ought to be first; reversed in order or arrangement; inverted.
Foolish; ridiculous; stupid; absurd.
Synonyms and Silly, Foolish, etc. (see absurd), monstrous, crazy, mad, wild, ludicrous. See foolish.
So unreasonable as to invite derision

Unjustified, Irresponsible, Perverse, Insane, Rational, Illogical, Reasonless, Yellow, Blind, Jaundiced, Superstitious, Incoherent, Unreasoning, Unreasonable, Nonrational

Farcical, Fallacious, Silly, Idiotic, Bizarre, Risible, Illogical, Outrageous, Laughable, Derisory, Foolish, Nonsensical, Ridiculous, Absurd, Ludicrous

Unjustified, Irresponsible, Perverse, Insane, Rational, Illogical, Reasonless, Yellow, Blind, Jaundiced, Superstitious, Incoherent, Unreasoning, Unreasonable, Nonrational

Farcical, Fallacious, Silly, Idiotic, Bizarre, Risible, Illogical, Outrageous, Laughable, Derisory, Foolish, Nonsensical, Ridiculous, Absurd, Ludicrous

So is there a magic answer about what exactly makes us irrational, and how those solutions designed for irrational humans are different?
When two irrational numbers are multiplied or divided, the product is sometimes rational and sometimes irrational.
When an irrational number and a rational number are added or subtracted, the sum is irrational.
The product of a rational number and an irrational number is SOMETIMES irrational.
When the square root of an irrational number is taken, does it have to be irrational?
Irrational love and irrational hate jostling together in the heart of that tormented man.
The product of two irrational numbers, in some cases, will be irrational.
Prove or disprove that the product of two irrational numbers is irrational.
Predictably Irrational, behavioral economist Dan Ariely claims that irrational.
The sum of an irrational number and an irrational number is irrational.

It is completely preposterous to just "start" school.
Gay is preposterous as a term describing them.
Department of English at Berkshire School is preposterous.
ED visit is preposterous and just plain wrong.
The Executive Order is preposterous in its irrationality.
Preposterous Pets: Lions, Bison and Bears, Oh My!
Wilkite movement, regarded as both preposterous and dangerous.
At one level, the sixth petition seems preposterous.
Preposterous as history, preposterous as drama, the show succeeds magnificently as bad television.
It travels through preposterous canyons on an even more preposterous trail.

What is a preposterous claim that would be a year ago?
Is Schatz buying the Missouri congressman's 'preposterous and ridiculous' revolt?