This lesson is optional because it revisits below gradelevel content. If the preunit diagnostic assessment indicates that your students know this material, this lesson may be safely skipped.
In this lesson, students review square and cube roots in a geometric context. The positive square root of a positive number \(a\) can be interpreted as the side length of a square with area \(a\), and the cube root of a positive number \(b\) can be interpreted as the edge length of a cube with volume \(b\). Algebraically, \(\sqrt{a}\) is interpreted as a solution to the equation \(x^2=a\) and \(\sqrt[3]{b}\) as a solution to \(x^3=b\). Through repeated calculations, students see patterns in the relationships between numbers and their roots (MP8). Viewing square and cube roots as solutions to quadratic and cubic equations will play an important role in upcoming lessons in which students use the graphs of \(y=x^2\) and \(y=x^3\) to think about square and cube roots more precisely.
In the next lesson, students will use exponent rules they reviewed in the previous lesson to connect square and cube roots to exponents that are unit fractions.
Lesson overview
 2.1 Warmup: It’s a Square (5 minutes)

2.2 Optional Activity: Squares and Their Side Lengths (15 minutes)
 Includes "Are you Ready for More?" extension problem
 2.3 Optional Activity: Cube It (15 minutes)
 Lesson Synthesis
 2.4 Cooldown: What is a Square Root? (5 minutes)
Learning goals:
 Comprehend the meaning of square roots and cube roots.
 Determine side lengths of squares and cubes, and express their exact values using radicals.
Learning goals (student facing):
 Let’s think about square and cube roots.
Learning targets (student facing):
 I can calculate square and cube roots.
Standards:
 This lesson builds on the standards:CCSS.8.EE.A.2MS.8.EE.2MO.8.EEI.A.2aMO.8.EEI.A.2bCCSS.8.NS.A.2MS.8.NS.2MO.8.NS.A.2
 This lesson builds towards the standards:CCSS.HSNRN.A.1MS.NRN.1MO.A2.NQ.A.1CCSS.HSNRN.A.2MS.NRN.2MO.A1.NQ.A.2
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