Perfect Squares, Cubes & Roots

Perfect squares, perfect cubes, and their roots extend students' number sense into new territory. They discover that 144 = 12 × 12 so √144 = 12, and that 125 = 5 × 5 × 5 so the cube root of 125 is 5 — these operations are inverses. Estimating √50 by locating it between √49 and √64 builds the number-line thinking that underpins all real-number work.