In this question you must show detailed reasoning.
Express 292\displaystyle 2^{\frac{9}{2}}229 in the form aba\sqrt{b}ab, where a a\,a is an integer and b b\,b is a prime number.
Express 32−23\displaystyle \frac{\sqrt{3}}{2-2\sqrt{3}}2−233 in the form c+dec+d\sqrt{e}c+de, where c c\,c and d d\,d are rational numbers and e e\,e is a prime number.