In this question you must show detailed reasoning.
Express 5112\displaystyle 5^{\frac{11}{2}}5211 in the form aba\sqrt{b}ab, where a a\,a is an integer and b b\,b is a prime number.
Express 221+2\displaystyle \frac{2\sqrt{2}}{1+\sqrt{2}}1+222 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.
134 exam-style questions on Edexcel AS Level Maths Algebraic Expressions, covering 1.1 Index Laws, 1.2 Expanding Brackets, 1.3 Factorising, 1.4 Negative and Fractional Indices, and 1.5 Surds. Each one has a worked solution and a mark scheme showing where the marks go.