Course 3 Online!
Henrico County Public Schools, Virginia
8.5 - Square Roots
Number and Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Computation and Estimation
Focus: Practical Applications of Operations with Real Numbers

The student will
a)   determine whether a given number is a perfect square; and
b)   find the two consecutive whole numbers between which a square root lies. 
Essential Knowledge and Skills 
  • Identify the perfect squares from 0 to 400.
  • Identify the two consecutive whole numbers between which the square root of a given whole number from 0 to 400 lies (e.g.,square root of 57  lies between 7 and 8 since 72 = 49 and 82 = 64).
  • Define a perfect square.
  • Find the positive or positive and negative square roots of a given whole number from 0 to 400. (See Curriculum Guide or Framework for symbols).
Essential Understandings
  • How does the area of a square relate to the square of a number? The area determines the perfect square number. If it is not a perfect square, the area provides a means for estimation.
  • Why do numbers have both positive and negative roots? The square root of a number is any number which when multiplied by itself equals the number. A product, when multiplying two positive factors, is always the same as the product when multiplying their opposites (e.g., 7 ∙ 7 = 49 and  -7 ∙ -7 = 49).
Vertical Articulation
  1. SOL 6.5 - investigate/describe positive exponents, perfect squares
  2. SOL 7.1a - investigate/describe negative exponents for the powers of 10
  3. SOL 7.1d - determine square roots
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Perfect Squares and Square Roots (PDF) - Working with perfect squares and square roots (Word)
  2. Notes: Square Roots and Perfect Squares (flipchart)
  3. Notes: Square Roots and Perfect Squares (doc)
  4. Notes: Estimating Square Roots with Practice (pdf)
  5. Guided Notes: Squares and Square Roots (doc)
  6. Activity: Square Roots Number Line (doc)
  7. VDOE Algebra Readiness Curriculum Companion: Exploring Whole Numbers (pdf)
Real World Lessons
  1. Quiz: Squares and Square Roots (doc)
  2. Worksheet: Square Root Word Problems (doc)
  3. Worksheet: Square Roots Practice (doc)
  1. SOL 8.5 Mini-Quiz: Square Roots
  1. Mathematics Assessment Project
    • A06:Sidewalk Patterns - Apprentice - In Prague some sidewalks are made of small square blocks of stone. The blocks are in different shades to make patterns that are in various sizes. In this task, you will look for rules which let you work out how many blocks of different colors are needed to make different sized patterns. (This task is very similar to Sidewalk Stones, but offers more step-by-step guidance.)
    • E13:Sidewalk Stones - Expert - This task is very similar to Sidewalk Patterns, but offers less step-by-step guidance.
  1. Khan Academy: Approximating Square Roots
  2. LearnAlberta: Exploring Square Roots Video (Video Interactive)
  3. PH: Simplifying square roots
Explore Learning
  1. None


VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Exploring Whole Numbers - The lessons focus on solving problems that use whole number operations, prime and composite numbers, odd and even numbers, perfect squares and square roots. (pdf)
Common Core Standards