Question

4- Зroot2/5 prove that it is irrational number​

Answer 1

Answer:

Step-by-step explanation:

Consider, 4−5√2

Let 4−5√2 = (a/b) a rational number

⇒ −5√2 = (a/b) − 4

⇒ −5√2 = (a − 4b)/b

⇒ √2 = (a − 4b)/(−5b)

Since a, b are integers, then (a − 4b)/(−5b) represents a rational number.

But this is a contradiction since RHS is a rational number where as LHS (√2) is an irrational number

Hence our assumption that " 4−5√2 = (a/b) is a rational number" is incorrect.

Thus 4−5√2 is an irrational number