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What is one example of an irrational number and a rational number?

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A rational is a number which could be written in the form of p/q or fraction. For Example \[\sqrt{4}\] = 2 which is understood 4/1. So \[\sqrt{4}\] is a rational number and \[\sqrt{3}\] is an irrational number.
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To prove that a number is irrational we usually assume it is rational and then prove it leads to a contradiction.

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Other answers:

also a rational number can be written as a fraction e.g. 2/3 whereas an irrational cannot many square roots are irrational like sqrt2 , sqrt5, sqrt7
Any squareroot of a prime is irational
right - also square root of some even numbers like 8, 12
That you get by writing those numbers as a multiplication of primes: 8=2*2*2, 12=2*2*3 and what is left in the squareroot is a prime, therefore irrational

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