Question

Are there two distinct irrational numbers such that their difference is a rational number? Justify​

Answer 1

Step-by-step explanation:

4+

2

,2+

2

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator and the denominator are whole numbers.

On the other hand, all numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.

So, let us take two irrational numbers a=4+

2

and b=2+

2

and we now calculate a−b as follows:

a−b=(4+

2

)−(2+

2

)=4+

2

−2−

2

=2=

1

2

Therefore, the difference of two irrational numbers a and b is 2 and from the above defination of rational numbers, we get that 2 is a rational number.

Hence, the difference of two irrational numbers 4+

2

and 2+

2

is a rational number.