Difference between Irrational and Insane

IRRATIONAL vs INSANE: NOUN

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.
A prime number.
An irrational number.
A real number that can not be expressed as the quotient of two integers, an irrational number.
That which is devoid of reason, as one of the lower animals.

Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; -- of assertions and beliefs.
Not rational; void of reason or understanding.
Of or relating to an irrational number.
Not consistent with or using reason
Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.
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.
Real but not expressible as the quotient of two integers
Being a metric foot containing such a syllable.
Of a real number, that cannot be written as the ratio of two integers.
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.

Characterized by insanity or the utmost folly; chimerical; unpractical
Causing insanity or madness.
Used by, or appropriated to, insane persons.
Exhibiting unsoundness or disorder of mind; not sane; mad; deranged in mind; delirious; distracted. See insanity, 2.
Very foolish; absurd.
Immoderate; wild.
Having been determined to be in a condition that meets the legal definition of insanity.
Intended for use by such persons.
Characteristic of or associated with persons who are mentally deranged.
Of, exhibiting, or afflicted with mental derangement. Not used in psychiatric diagnosis.
Very foolish
Afflicted with or characteristic of mental derangement

In Greek prosody, incapable of measurement in terms of the fundamental or primary time or metrical unit.
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.

Synonyms Crazed, lunatic, demented, maniacal.
Making insane; causing insanity.
Devoted to the use or care of the insane: as, an insane asylum.
Characteristic of a person mentally deranged; hence, wild; insensate; senseless.
Not sane; unsound or deranged in mind; crazy.

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

Nutty, Schizophrenic, Paranoid, Loony, Batty, Maniac, Psychotic, Unhinged, Deranged, Demented, Idiotic, Mad, Bonkers, Lunatic, Crazy

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

Nutty, Schizophrenic, Paranoid, Loony, Batty, Maniac, Psychotic, Unhinged, Deranged, Demented, Idiotic, Mad, Bonkers, Lunatic, Crazy

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.

This whole situation is insane and quite frankly is making me insane.
This is one insane quest fit for one insane faction of isolated geniuses.
Even if not deemed legally insane, a serial killer is certainly morally and ethnically insane.
If you want to demonstrate that someone is insane, then they gotta fucking look insane.
He acts insane but tries to insist I am the one who is insane.
Do people living through insane times realize just how insane that time is?
Asa was insane; but Asa was insane because the deed itself was insane.
Finally, I went insane, and not the good kind of insane either.
The people are all insane, the other animals are all insane, the earth is insane, Nature itself is insane.
Insane stunting circuits, insane jumps, insane speeds: Trackmania Turbo has it all.