## Irrational and Rational Numbers

Expressions may look irrational yet still be rational. For example:
• (3 + 7^(1/2) - (8 - 2*7^(1/2))^(1/2))^(1/2) = 2, a rational #
• (8 + 11^(1/2) - (12 - 2*11^(1/2))^(1/2))^(1/2) = 3, a rational #
Is there a way to generalize these two examples?

On a side note: How would I write these two examples so that they are expressed using a square root symbol as opposed to ^(1/2) so that they look... prettier?