Students compute and write square root and cube root expressions using the symbols √ and ∛ (for example, √4 = 2 and ∛27 = 3). Student activity pages and answer keys require evaluating square roots of small perfect squares and cube roots of small perfect cubes (e.g., √9, √16, √25, ∛27, ∛64, ∛125, √196, ∛1000). Students learn to use a calculator to compute roots and to follow steps that place the root symbol over a number, reinforcing symbolic representation of roots.

Students use square root and cube root notation throughout: they evaluate √16 = 4, √9, √121, √100 and cube roots such as ∛27, ∛64, ∛8 and the cube root of 125 on the review. Students practice interpreting roots as the number whose square or cube gives the radicand (e.g., √25 = 5 because 5×5 = 25) and use radicals when comparing and ordering values (e.g., squaring √30 to get 30 to place it between 5 and 6). Students approximate √2 and other non-perfect square roots to two decimal places and are explicitly told and shown that √2 is irrational.

Students are asked in Phase 2 to classify √2 micrometers and 1.75 micrometers as rational or irrational and to justify their answers. The Activity also asks students to determine whether √50 is rational or irrational. The answer key explicitly states that √2 and √50 are irrational and the parent notes emphasize identifying rational and irrational numbers.

Students are asked to evaluate square roots and cube roots in multiple problems (e.g., find √81, √144, cube root of 27, cube root of 64). Several items ask students to approximate nonperfect roots and decide rationality (e.g., approximate √45 and √75, determine whether √50 or √45 is rational or irrational). The Parent Plan explicitly states students should "Use square root and cube root symbols to solve equations like x² = p or x³ = p" and notes that students should "Know that √2 is an irrational number," including an example of approximating √2 by truncating its decimal expansion.

The Parent Plan Skills list explicitly states that students will "Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p." In Task 1 (Drop Zone Radius) students are instructed to use A = πr² and solve for the radius, which requires taking a square root (r = sqrt(A/π)). In Task 2 (Distance from Depot) students are told the distance is given as a square root and must determine that distance to the nearest hundredth without a calculator, requiring evaluation of a square root expression.

Students are asked to find cube roots (e.g., "Find the cube root of 27") and to identify and evaluate square roots in several questions (e.g., items asking to compare √5 to 2.2 and to classify √4, √9, √10 as rational or irrational). The Skills Review explicitly includes a prompt to "Explain why √2 is an irrational number," and the answer key states that √2 is irrational. The answer key also gives the cube root of 27 = 3 and lists √4 and √9 as rational, showing evaluation of small perfect squares and cubes.

Students work with squaring as an operation when they complete a function table whose rule is "the output is the result of squaring a number and then subtracting two" (x-values 0,1,2,3 producing y-values -2,-1,2,7). The parent/instruction text and multiple-choice items also reference quadratic expressions (e.g., identifying y = x^2 + 2 as nonlinear) and give examples using A = s^2 with points (1,1), (2,4), (3,9).

Students solve equations of the form a^2 + b^2 = c^2 and then take square roots to find unknown side lengths (e.g., 25 = c^2 → c = 5; 144 = a^2 → a = 12). Multiple activity pages and answer keys show students evaluating square roots of perfect squares (e.g., √576 = 24, √144 = 12, √25 = 5). The materials also use square-root notation in worked answers (e.g., √(26^2 − 10^2) = √576) and ask students to "find the square root" as a final step.

Students solve equations that require taking cube roots and square roots to find radii and heights (for example, 64 = r^3 is solved to get r = 4 in the sphere example). Activity problems and answer keys ask students to find r from volume formulas that lead to r^2 = p or r^3 = p (several cylinder, cone, and sphere problems require solving r^2 or r^3). Students compute small perfect squares and cubes when they square and cube radii in example calculations (e.g., 3^2 = 9, 3^3 = 27, 4^3 = 64).

Students compute hypotenuses using square roots in Pythagorean problems (answer key shows √(36 + 64) = √100 = 10 and √(81 + 144) = √225 = 15). Several volume problems require solving equations that lead to cubic equations for radius (answer key gives r³ = 64 → r = 4 and sphere/cone volume problems with integer radii such as 3 cm). The answer keys and worked solutions display the square root symbol when evaluating perfect squares.

Students solve explicit root equations in Part 2 of the "Exponents and Roots" activity: they evaluate √49 and solve x^2 = 81 (x = 9) and x^3 = 125 (x = 5). The Exponents and Roots page asks students to decide when to use exponents or roots and to write answers in simplified form, and the answer key shows evaluation of small perfect squares and perfect cubes. Activity 4 has students classify numbers as rational or irrational and approximate square roots of nonperfect squares (e.g., √15, √20), and the Skills/Things to Know section explicitly states that students should know √2 is irrational and gives the example of approximating √2 by truncating its decimal expansion.

Students are asked to evaluate square roots using the radical symbol (Question 11: "What is the square root of 196?" and Question 12: "Estimate √30 to the nearest hundredth."). The answer key gives √196 = 14 and √30 ≈ 5.48, showing students practice computing a perfect-square root and estimating a nonperfect square using the √ notation. The assessment also includes items distinguishing rational and irrational numbers elsewhere, indicating some work with number classification.

Students compute hypotenuses using the Pythagorean Theorem (e.g., 9^2 + 12^2 = 225 → c = 15) and find distances between points (distance between (0,0) and (6,8) = 10). One problem verifies 8^2 + 15^2 = 289 and uses √289 = 17, and the sphere-volume problem leads students to solve r^3 = 64 and conclude r = 4. These tasks require evaluating square roots of perfect squares and cube roots of perfect cubes in numeric problem solving.