Answer:
Consider,
x = 4 – 5√2 be a rational number.
x = 4 – 5√2
x2 = (4 – 5√2)2
x2 = 42 + (5√2)2 – 2(4) (5√2)
x2 = 16 + 50 – 40√2
x2 – 66
x2 = – 40√2
=> 
=> √2
x is a rational number, x2 is also a rational number.
⇒ 66 – x
2 is a rational number
√2 – rational number
But √2 is an irrational number, which is a contradiction.
The assumption is wrong.
Hence, (4 – 5√2) is an irrational number.