Question

can the sum of two irrational numbers ever be a rational number? Can the quotient of two irrational numbers ever be a rational number? Explain with examples.

Answer 1

Yes, both can be rational numbers.

Explanation:

Answer 2

Yes, both can be rational numbers.

Explanation:

The sum of two irrationals can be rational.

Example:

`√(2)` is irrational,

and so is
`1 + √(2)` and
`1 - √(2)`

`(√(2)+1) + (√(2)-1) = 2`

The sum is rational because the irrational numbers can cancel out.

The quotient of two irrational numbers can also be rational.

Example:

`√(2)` is irrational.

`(√(2) )/(√(2) ) = 1`