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 of real number work.
What students explore
Square roots and perfect squares extend students' number sense into a new territory. They discover that 144 = 12 × 12 and so √144 = 12 — squaring and square-rooting are inverses. Estimating √50 by locating it between √49 and √64 builds the number-line thinking that underpins all of real number work.
Key ideas
Identify perfect squares to 225. Determine the square root of a perfect square. Estimate the square root of a non-perfect square to the nearest tenth. Explain the relationship between squaring and taking a square root.
Putting it together
Apply these ideas through worked examples, guided practice, and real-world problems.