Some numbers such as pi, e, and square roots are used quite commonly. Whether you use them at all will depend on what you do in your everyday life, of course. Engineers might use them commonly; others not so much.Even for an engineer, or ESPECIALLY for an engineer, the distinction between rational and irrational is irrelevant for most practical purposes; for instance, if you round pi, or the square root of 2 (which are both IRRATIONAL), to 10 or 15 significant digits, you get a RATIONAL number - and the resulting precision is more than enough for most purposes. (In fact, if you round to ANY number of digits, the result will still be rational.)
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The diagonal of a square with unit sides is an irrational number. pi, which is a key constant in geometry and calculus, is irrational. Euler's number, e, which is a fundamental constant in slightly more advanced calculus is irrational. Irrational Numbers appear all over the in everyday life.
An imaginary number i is defined as the square root of -1, so if you have something like the square root of -2, the answer would be i root 2, and that would be considered an irrational non-real number.* * * * *Not quite. The fact that irrational coefficients can be used, in conjunction with i to create complex numbers (or parts of complex numbers) does not alter the fact that all irrational numbers are real numbers.
Algebra is used in lots of differant ways in everyday life because it's maths.
There is no specific symbol. The symbol for real numbers is R and that for rational numbers is Q so you could use R \ Q.
There are different methods for estimating irrational numbers. For numbers like pi or e, there are infinite series which can be used to calculate their value to the required degree of accuracy. There are numerical methods - such as the Newton-Raphson iteration - for estimating roots of numbers.
Signed numbers are used for:TemperatureMoney, Accounting, or EconomyMath Problems