Understanding Square Roots and Perfect Squares

This lesson introduces the concept of square roots, focusing on numbers that are not perfect squares. It explains how to estimate and place these square roots between two integers on a number line. The lesson covers the properties of perfect squares, the use of the square root symbol, and provides examples to illustrate the concepts. Students learn to identify the closest perfect squares to estimate the square roots of non-perfect squares, such as radical 11 and radical 122.

What is a perfect square?

• A number that can be formed into a square using unit squares

• A number that is always odd

• A number that is less than 10

• A number that can be divided by 2

What symbol is used to represent a square root?

• The multiplication sign

• The plus sign

• The division sign

• The radical sign

Why can't the number 5 be a perfect square?

• Because it is an odd number

• Because it cannot form a perfect square with integer side lengths

• Because it is less than 10

• Because it is a prime number

What is the estimated square root of 5?

• 4

• 2.1

• 2

• 3

How do you find the two integers between which a non-perfect square root lies?

• By using a calculator

• By finding the closest perfect squares

• By dividing the number by 2

• By guessing

Between which two integers does the square root of 11 lie?

• 5 and 6

• 2 and 3

• 3 and 4

• 4 and 5

What is the square root of 100?

• 12

• 10

• 11

• 9

Which letter best represents the location of radical 122 on a number line?

• D

• C

• A

• B

What is the square root of 121?

• 13

• 10

• 11

• 12

What have you learned about numbers that are not perfect squares?

• They are always greater than 100

• They are always even

• They have square roots that can be placed between two integers

• They do not have square roots