Students will learn to simplify the \(n\)-th root of an integer \(x\) using the prime factorization of \(x.\) Conclude this lesson by giving your students this challenge. Students may find the solution by trial and error, or they might find the solution in the same way as the last solution on the NRICH page. The latter solution is unlikely to be found by students, because it requires a creative step they've likely never taken before. However, the solution is not complicated, and I think there's value in showing students the reasoning, whether or not they found the solution in this way.
Next, give your students these challenges:
Conclude by leading this investigation:
Number Guessing Game – algebra