**Richard Mills** and **Tung Tran**, secondary school teachers in north London, devised the prompt during a school training day when they were collaboratively planning an inquiry lesson. Once the class verifies the truth of the prompt, the inquiry could lead into finding similar statements. Students could set themselves the target of finding a surd that is a third of another, a quarter of another and so on. For example, **√(27) is a third of √(243)** and **√(8) is a quarter of √(128)**. A further challenge sees students looking for a surd that is two-thirds or three-quarters of another. For the first case, **√(216) is two-thirds of √(486)**.