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Irrational numbers can be roots because they are solutions to certain mathematical equations. For example, the square root of 2 is an irrational number that is a solution to the equation x^2 = 2. Similarly, other irrational numbers can be roots of different equations depending on their mathematical properties.
There is no simple factorisation because the quadratic expression does not have rational roots. Irrational roots are not used in factorisation.
A rational expression is an expression that includes only additions, subtractions, multiplications and divisions. Some of the things that will make an expression irrational (not rational) are square roots, higher-level roots, non-integer powers, exponentials (powers in which the variable expression occurs in the exponent), and common functions such as logarithms or trigonometric functions.
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