Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities

Functions

Statistics

SOL Review Materials
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
  1. SOL 7.1 - d) determine square roots
  2. 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
  1. VDOE ESS Lesson: Simplifying Square Roots - Expressions and Operations (PDF) - Simplifying square roots (Word)
  2. VDOE ESS Lesson: Simply Radical - Expressions and Operations (PDF) - Simplifying square roots and cube roots of algebraic expressions (Word)
  3. Notes: Simplifying Radicals (ppt)
  4. Notes: Simplifying Square Roots and Cube Roots (flipchart)
  5. Notes: Simplifying Radicals with Non-Perfect Squares (flipchart)
  6. Extension: Operations with Radicals (ppt)
Real World Lessons
Practice
  1. Worksheet: Radicals CW (doc)
  2. Worksheet: Radicals HW (doc)
  3. ExamView Quiz: Pythagorean Theorem
  4. Prentice Hall Quiz - Square Roots
  5. Prentice Hall Quiz - Pythagorean Theorem
Self-Assessments
Skills
Videos
  1. Video: PH Using the Pythagorean Theorem to Find the Hypotenuse
  2. Video: PH Using the Pythagorean Theorem to Find the Leg
  3. Video: PH Using the Converse of the Pythagorean Theorem
  4. NFL Football explains the Pythagorean Theorem
  5. Video: PH Simplifying Square Roots
  6. Video: PH Estimating Square Roots of Rational Numbers
  7. Video: PH Simplifying Radical Expressions with Products
Explore Learning
  1. Simplifying Radical Expressions - Activity A - Simplify a radical expression. Use step-by-step feedback to diagnose any incorrect steps.
  2. Simplifying Radical Expressions - Activity B - Simplify radical expressions. Use step-by-step feedback to diagnose incorrect steps.
  3. 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
  1. Wisc-Online: A Visual Approach To Simplifying Radicals
  2. Interactive Notes: Pythagorean Theorem - lessons and practice problems atRegentsprep.org
  3. 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
8.NS.2
8.EE.2