An irrational number has a never-ending decimal expansion. To estimate it's value, you'd just state the expansion to some number of digits.
Ex:
sqrt(2) is approximately 1.4142135623730950488
pi is approximately 3.14159265358979323846
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If you want to use a rational number for a mathematical operation, it will be necessary to estimate it for a numerical outcome. Irrational numbers can't be written out exactly.
How an irrational number is estimated depends on the nature of the number. The reason for estimating them is that two of the most important numbers in mathematics: pi in geometry and e in calculus, are both irrational. Also, the diagonal of a unit square is of length sqrt(2), an irrational. Irrational numbers crop up everywhere: there are more irrational numbers than there are rational.
An irrational number.
When added to a rational number, any irrational number will produce an irrational number.also, when added to an irrational number, any rational number will produce an irrational number.
It is not an irrational number!