The correct option is D Real number
Check for Irrational number: Let's assume 5√4 is a rational number and its fractional form is pq, where p and q are integers, q≠0 and p and q have no common factors other than 1.
(raising fifth power on both sides)
Here, p should be an even number as p5 is an even number.
(substituting this value in the original expression)
∴q should also be an even number, which contradicts the assumption that p and q do not share any common factors other than 1.
Hence, 5√4 is an irrational number.
Check for Surd: nth root of a number which can not be simplified into a rational number is called surd.
Here 5√4 can not be simplified into a rational number hence, it is a surd.
Check for Quadratic Surd: Square root of any non-perfect square is called quadratic surd.
5√4 is not a quadratic surd as the 5th root is not a square root.
Also, an irrational number is a real number.