Real Number System: Estimating Square Roots

Multiple Choice

Which of the following statements best describes a square root?

• A number that, when multiplied by itself, equals the given number.

• A number that is always positive.

• A number that is always negative.

• A number that is always an integer.

Multiple Choice

Which of the following numbers is a perfect square?

• 8

• 15

• 25

• 18

Multiple Choice

Which of the following statements are true about the square roots of positive numbers?

• Every positive number has only a positive square root.

• Every positive number has only a negative square root.

• Every positive number has both a positive and a negative square root.

• Every positive number has no square root.

Multiple Choice

What is the definition of a perfect square?

• A number whose square root is a fraction

• A number whose square root is a decimal

• A number whose square root is an integer

• A number whose square root is a negative number

Open Ended

What are the positive and negative square roots of 36?

Multiple Choice

Which of the following numbers is NOT a perfect square?

• 49

• 81

• 100

• 120

Open Ended

What is a perfect square, and how is it related to the area of a square?

Multiple Choice

What is the exponent form of the perfect square 81?

• 8^2

• 9^2

• 81^2

• 3^4

Multiple Select

Select all the numbers that are perfect squares from the following: 64, 90, 121, 150.

• 64

• 90

• 121

• 150

Multiple Select

Which of the following numbers are perfect squares?

• 16

• 20

• 25

• 30

Multiple Choice

Which of the following is a perfect square?

• 49

• 50

• 45

• 60

Multiple Choice

If the area of a square is 49 in², how long is each side?

• 7 in

• 14 in

• 24.5 in

• 9 in

Open Ended

Explain how you would find the side length of a square if you know its area is 225 square inches.

Open Ended

Describe the steps you would take to estimate the square root of a number that is not a perfect square, such as 29.

Multiple Select

Select all the steps involved in finding the two consecutive integers between which the square root of a non-perfect square lies.

• Determine if the number is a perfect square

• Find the largest perfect square less than the number

• Find the smallest perfect square greater than the number

• Divide the number by 2

Multiple Choice

Which of the following is a perfect square less than 29?

• 25

• 16

• 9

• 36

Multiple Choice

What is the value of √36?

• 6

• 5

• 7

• 8

Open Ended

Explain the steps to determine between which two integers the square root of a non-perfect square number lies, using 29 as an example.

Multiple Choice

What are the two consecutive integers between which the square root of 29 lies?

• 5 and 6

• 4 and 5

• 6 and 7

• 4 and 6

Open Ended

Find the two consecutive integers between which the square root of 19 lies.

Multiple Choice

Which of the following square roots is closest to the point labeled 'B' on the number line?

• √2

• √10

• √60

• √83

Open Ended

After learning about positive and negative square roots, do you have any questions or topics you would like to explore further?