B2.2 · Recall common square numbers and square roots

Ontario Grade 8 Mathematics

Number

Recognize equal rows and columns, then recall their number facts

What you will learn

• Recognize common square numbers made by multiplying a whole number by itself.
• Recall the matching whole-number square roots for square numbers from 1 through 144.
• Use known square-number facts to find a missing value in a short list.

1. Build a square number

• A square array has the same number of rows and columns.
• The raised 2 means multiply a number by itself.
• A square root tells which whole number makes the square number when multiplied by itself.

2. Recall common square numbers

• Recall the square numbers made by whole numbers from 1 through 12.
• Match each square number with its whole-number square root.
• Check a remembered fact by multiplying the root by itself.

3. Use known facts

• Multiplication confirms a square number.
• The matching fact confirms a square root.
• Use the common-number list to recognize square numbers.

Common square numbers and their square roots

Worked example

Example 1: Count a square array

1. Use the row and column count
   There are 7 rows and 7 columns. The total is 7 multiplied by itself, which is the square-number fact for 7.
   $$7^2=7\times7$$
2. Find the total
   Multiplying gives 49 objects. The total is a square number because it comes from a square array with 7 rows and 7 columns.
   $$7\times7=49$$
3. Find the matching root
   The square root of 49 is 7, because 7 multiplied by itself gives 49.
   $$\sqrt{49}=7$$

Worked example

Example 2: Recall a square root

1. Find the matching square fact
   The square-number fact for 11 is that 11 multiplied by itself is 121. This matches the number under the square-root sign.
   $$11^2=121$$
2. State the root
   Since 11 multiplied by itself gives 121, the square root of 121 is 11.
   $$\sqrt{121}=11$$

Worked example

Example 3: Fill in a missing square number

1. Match the known square numbers
   The list begins with the squares of 6 and 7, and ends with the square of 9. The missing square number is the square for 8.
   $$6^2=36,\quad7^2=49,\quad9^2=81$$
2. Calculate the missing value
   Eight multiplied by itself is 64, so 64 belongs in the blank.
   $$8\times8=64$$
3. Give the matching root
   The square root of 64 is 8 because 8 multiplied by itself gives 64.
   $$\sqrt{64}=8$$

Common mistakes and how to avoid them

Lesson summary

• A square number is made by multiplying a whole number by itself.
• A square root tells which whole number was multiplied by itself to make the square number.
• Recall common facts such as $8^2=64$ and $\sqrt{64}=8$.
• Check a square-root answer by multiplying the root by itself.

Check your understanding

Key terms

Square number

A number made by multiplying a whole number by itself, such as $6\times6=36$.

Square root

The whole number that, when multiplied by itself, gives a stated square number. For example, $\sqrt{36}=6$.

Square array

An arrangement with the same number of rows and columns.

Continue through Grade 8 Math

View the complete Grade 8 Math Ontario Grade 8 Mathematics curriculum and lessons

• B2.1 · Solve multistep rational-number, ratio, rate, and percent problems
• B2.3 · Multiply and divide decimals mentally by powers of ten
• B1.1 · Represent and compare very large and small numbers using scientific notation
• B1.2 · Describe and order rational and irrational numbers
• B1.3 · Estimate and calculate square roots
• B2.4 · Add and subtract integers in context

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation B2.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

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