A.3 
The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form. 

Essential Knowledge and Skills 
 A square root in simplest form is one in which the radicand (argument) has no perfect square factors other than one.
 A cube root in simplest form is one in which the argument has no perfect cube factors other than one.
 The cube root of a perfect cube is an integer.
 The cube root of a nonperfect cube lies between two consecutive integers.
 The inverse of cubing a number is determining the cube root.
 In the real number system, the argument of a square root must be nonnegative while the argument of a cube root may be any real number.

Essential Understandings 
 Express square roots of a whole number in simplest form.
 Express the cube root of a whole number in simplest form.
 Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values.


Vertical Articulation 
 SOL 7.1  d) determine square roots
 SOL 8.5  a) determine if a number is a perfect square; b) find two consecutive whole numbers between which a square root lies

Instructional Materials 
 VDOE ESS Lesson: Simplifying Square Roots  Expressions and Operations (PDF)  Simplifying square roots (Word)
 VDOE ESS Lesson: Simply Radical  Expressions and Operations (PDF)  Simplifying square roots and cube roots of algebraic expressions (Word)
 Notes: Simplifying Radicals (ppt)
 Notes: Simplifying Square Roots and Cube Roots (flipchart)
 Notes: Simplifying Radicals with NonPerfect Squares (flipchart)
 Extension: Operations with Radicals (ppt)

Real World Lessons 

Practice 
 Worksheet: Radicals CW (doc)
 Worksheet: Radicals HW (doc)
 ExamView Quiz: Pythagorean Theorem
 Prentice Hall Quiz  Square Roots
 Prentice Hall Quiz  Pythagorean Theorem

SelfAssessments 

Skills 

Videos 
 Video: PH Using the Pythagorean Theorem to Find the Hypotenuse
 Video: PH Using the Pythagorean Theorem to Find the Leg
 Video: PH Using the Converse of the Pythagorean Theorem
 NFL Football explains the Pythagorean Theorem
 Video: PH Simplifying Square Roots
 Video: PH Estimating Square Roots of Rational Numbers
 Video: PH Simplifying Radical Expressions with Products

Explore
Learning 
 Simplifying Radical Expressions  Activity A  Simplify a radical expression. Use stepbystep feedback to diagnose any incorrect steps.
 Simplifying Radical Expressions  Activity B  Simplify radical expressions. Use stepbystep feedback to diagnose incorrect steps.
 Square Roots  Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number.

Websites 
 WiscOnline: A Visual Approach To Simplifying Radicals
 Interactive Notes: Pythagorean Theorem  lessons and practice problems atRegentsprep.org
 Interactive: Pythagorean Explorer  find the length of a side of a right triangle by using the Pythagorean Theorem at Shodor.org

Old Website Links 

Common Core
Standards 
