In this question you must show detailed reasoning.
Express 372\displaystyle 3^{\frac{7}{2}}327 in the form aba\sqrt{b}ab, where a a\,a is an integer and b b\,b is a prime number.
Express 53−35\displaystyle \frac{\sqrt{5}}{3-3\sqrt{5}}3−355 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.
233 exam-style questions on Edexcel A 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.