Question

IS THE SUM OR DIFFERENCE OF A RATIONAL AND IRRATIONAL NUMBER ? JUSTIFY

Answer 1

Answer:

Step-by-step explanation:

The sum or difference of a rational and irrational number is irrational.

Prove : Let x be a rational number and

            y be an irrational number

Assume x+y as a rational number

x = rational number

(x + y) - (x) = y is a rational number

x = 2  y = √2

2 + √2 - 2 = √2 = rational number (as per assumption)

But this contradicts the fact that y is an irrational number and x+y is also an irrational number.