Question

When a and b are natural numbers `(sqrt(a) + sqrt(b)) (sqrt(a) - sqrt(b))` is ______.

Options

• rational

• irrational

• not real

• can be rational or irrational

Answer 1

When a and b are natural numbers `(sqrt(a) + sqrt(b)) (sqrt(a) - sqrt(b))` is rational.

Explanation:

The expression 

`(sqrt(a) + sqrt(b))(sqrt(a) - sqrt(b))`

= `(sqrt(a))^2 - (sqrt(b))^2`

= a – b

Here, a and b are natural numbers, so a – b is a whole number, possibly positive, zero or negative.

But the key point is a – b is always rational, since it’s the difference of two natural numbers.