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We all know the the square root of 2 is irrational. So, the answer should be no. But how do we prove it?Let's assume for contradiction that x²=2 and that x is rational. Then x can be expressed ...

Let's take a positive integer n.We can write it as a product of prime numbers:n=p₁p₂...p_r, where p₁, p₂, ..., p_r are prime factors of n.No...

Most students at GCSE are taught to use the structure of PEE (Point Evidence Explanation) in each of their paragraphs in order to construct their argument. However, A-level requirements differ, as exam...

Let's begin by reviewing a fairly simple (linear) equation:

(1) y = 2x + 3

(1) describes the relationship between two variables, <...

First, we use the idea that a complex number z can be written in terms of its real and imaginary parts, i.e. z = x+iy, to write our expression as:

| x+ iy -5 - 3i | = ...