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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 x 2 =2 and that x is rational. Then x can be expressed as a rationa...

Let's take a positive integer n.We can write it as a product of prime numbers:n=p 1 p 2 ...p r , where p 1 , p 2 , ..., p r are prime factors of n.Now, assume that n 2 is even. Then one of the p i equals 2. ...

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 examiners ...

Let's begin by reviewing a fairly simple (linear) equation: (1) y = 2x + 3 (1) describes the relationship between two variables, x and y . Given a value for one, we can use (1) to work out the value of the u...

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 | = 3 Next, we can group the real and imagin...