If the positive square root of (5+3\sqrt{2})(5-3\sqrt{2}) is a, then what is the positive square root of 8+2a?

Explanation

First, evaluate the product: (5+3\sqrt{2})(5-3\sqrt{2}) = 25 - 18 = 7. Thus, a = \sqrt{7}. The expression 8+2a = 8+2\sqrt{7} = (\sqrt{7})^2 + 1^2 + 2(1)(\sqrt{7}) = (\sqrt{7}+1)^2. Its positive square root is \sqrt{7}+1.

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