SOL Objective(s):
7.1 The learner will...
d) determine square roots.
8.5 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.
d) determine square roots.
8.5 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.
Previous and Related SOL Objectives: 
Prerequisite Skills: 
Khan Skill Phrases:Square Roots of Perfect Squares
Estimating Square Roots (Simplifying Square Roots) (Simplifying Square Roots 2) (Cube Roots) (Cube Roots 2) 
The Basics and Background Information
• A square root of a number is a number which, when multiplied by itself, produces the given number (e.g., square root of 121 is 11 since 11 x 11 = 121).
• The square root of a number can be represented geometrically as the length of a side of the square. • A perfect square is a whole number whose square root is an integer (e.g., The square root of 25 is 5 and 5; thus, 25 is a perfect square).
• The square root of a number is any number which when multiplied by itself equals the number.
• Whole 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).
• Any whole number other than a perfect square has a square root that lies between two consecutive whole numbers.
• The square root of a whole number that is not a perfect square is an irrational number (e.g., sqrt of 2 is an irrational number). An irrational number cannot be expressed exactly as a ratio.
• Students can use grid paper and estimation to determine what is needed to build a perfect square.
• The square root of a number can be represented geometrically as the length of a side of the square. • A perfect square is a whole number whose square root is an integer (e.g., The square root of 25 is 5 and 5; thus, 25 is a perfect square).
• The square root of a number is any number which when multiplied by itself equals the number.
• Whole 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).
• Any whole number other than a perfect square has a square root that lies between two consecutive whole numbers.
• The square root of a whole number that is not a perfect square is an irrational number (e.g., sqrt of 2 is an irrational number). An irrational number cannot be expressed exactly as a ratio.
• Students can use grid paper and estimation to determine what is needed to build a perfect square.
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
7th Grade:
• Determine the square root of a perfect square less than or equal to 400.
• Squaring a number and taking a square root are inverse operations.
8th Grade:
• 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., sqrt of 57 lies between 7 and 8 since 7^2 = 49 and 8^2 = 64).
• Define a perfect square.
• Find the positive or positive and negative square roots of a given whole number from 0 to 400. (Use the sqrt symbol to ask for the positive root and −sqrt when asking for the negative root.)
7th Grade:
• Determine the square root of a perfect square less than or equal to 400.
• Squaring a number and taking a square root are inverse operations.
8th Grade:
• 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., sqrt of 57 lies between 7 and 8 since 7^2 = 49 and 8^2 = 64).
• Define a perfect square.
• Find the positive or positive and negative square roots of a given whole number from 0 to 400. (Use the sqrt symbol to ask for the positive root and −sqrt when asking for the negative root.)
Vocabulary and Things to Know:

Be Able To:

The topic: What is it and what will we learn?
Recognize and simplify square roots as an operation.
Understanding Square Roots 

Simplifying RadicalsA bit more explanation than needed for our class, BUT... a really great explanation and a really great opportunity to know and understand more about finding square roots of nonperfect square roots.

