Question

Which one of the following statements is true?

Options

• The sum of two irrational numbers is always an irrational number

• The sum of two irrational numbers is always a rational number

• The sum of two irrational numbers may be a rational number or an irrational number

• The sum of two irrational numbers is always an integer

Answer 1

Since, `-sqrt2 and sqrt2 - 1` are two irrational number and  `-sqrt2+(sqrt2+1 = 1`

Therefore, sum of two irrational numbers may be rational Now, let `sqrt3 and sqrt2 - sqrt3 `be two irrational numbers and`sqrt3 +(sqrt2 - sqrt3) = sqrt2`

Therefore, sum of two irrational number may be irrational.