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"Sqr(2 + Sqr(3)) + Sqr(2 - Sqr(3)) works out to a simple radical (the square root of six). But not all radical expressions like that are so nice. How can you tell whether it'll simplify?" ~Paul
Hi Paul, whenever I have a question like this, I automatically think, "I'm going to replace the numbers with variables to see what happens."
So I'm going to rewrite your expression with variables, and then start manipulating it algebraically: