Pi an the square root of two
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A rational number is one that can be represented as an integer or a fraction with an integer over an integer. An irrational number cannot be represented using integers. Examples of rational numbers: 2, 100, 1/2, 3/7, 22/7 Examples of irrational numbers: π, e, √2
Numbers are either irrational (like the square root of 2 or pi) or rational (can be stated as a fraction using whole numbers). Irrational numbers are never rational.
No, the set of all irrational numbers is not countable. Countable sets are those that can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). The set of irrational numbers is uncountable because it has a higher cardinality than the set of natural numbers. This was proven by Georg Cantor using his diagonalization argument.
As the area of a rectangle is one side (length) multiples by the other (width), if either is irrational, then the area will be irrational. eg a rectangle with width 1 cm and diagonal 2 cm: using Pythagoras you can find out the length of the rectangle as √(2² - 1²) = √(4 - 1) = √3 which is irrational. The area of the rectangle is 1 cm × √3 cm = √3 cm² (which is irrational).
With great difficultly because it is an irrational number and it is about 14.69693846 by using a calculator