How do you approximate from a radical? - Answers

To approximate a value from a radical, you can use numerical methods such as the Babylonian method (or Newton's method) for square roots, which involves making an initial guess and refining it through iteration. For example, to approximate √N, start with a guess ( x_0 ) and apply the formula ( x_{n+1} = \frac{1}{2}(x_n + \frac{N}{x_n}) ) until the value converges. Alternatively, you can also use a calculator or estimate by identifying perfect squares near the radical for a rough approximation.