If the simplified form of an expression contains an irrational number and a numerical evaluation is required then it is necessary to use a rational approximation.
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A repeating decimal is a rational number. Its value is(the repeating set of digits)/(as many 9s as there are digits above).
That they can have any value: integer, rational, irrational or complex.
If the value applied in the radical is not a perfect square, it is irrational. 25; 400; and 625 are perfect squares and are rational when applied in a radical.
The exact value is an irrational number, and can't be written on paper with digits.0.34202 is less than 0.000042 percent wrong.Cos(70 deg) is an irrational number and it is impossible to give its exact value.
It is the decimal approximation to the value of the irrational number.