Understanding Square Roots and Consecutive Whole Numbers

The video tutorial explains how to determine which consecutive whole numbers a non-perfect square root lies between. It provides a list of perfect squares and demonstrates the process through four examples: square roots of 7, 32, 75, and 112. Each example shows how to identify the perfect squares surrounding the radicand and simplifies the square roots to find the consecutive whole numbers.

What is the main challenge when dealing with square roots of non-perfect squares?

• They are always greater than 10.

• They simplify to whole numbers.

• They are always less than 1.

• They do not simplify to whole numbers.

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Which two perfect squares is the square root of 7 between?

• 16 and 25

• 4 and 9

• 9 and 16

• 1 and 4

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What is the approximate value of the square root of 7?

• Between 4 and 5

• Between 3 and 4

• Between 2 and 3

• Between 1 and 2

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CCSS.8.NS.A.2

Which perfect squares are used to find the consecutive whole numbers for the square root of 32?

• 16 and 25

• 36 and 49

• 49 and 64

• 25 and 36

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What is the approximate value of the square root of 32?

• Between 4 and 5

• Between 6 and 7

• Between 5 and 6

• Between 7 and 8

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CCSS.8.NS.A.2

Which two perfect squares is the square root of 75 between?

• 100 and 121

• 81 and 100

• 64 and 81

• 49 and 64

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What is the approximate value of the square root of 75?

• Between 10 and 11

• Between 9 and 10

• Between 8 and 9

• Between 7 and 8

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CCSS.8.NS.A.2

Which perfect squares are used to find the consecutive whole numbers for the square root of 112?

• 81 and 100

• 100 and 121

• 144 and 169

• 121 and 144

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What is the approximate value of the square root of 112?

• Between 10 and 11

• Between 11 and 12

• Between 12 and 13

• Between 9 and 10

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Why is it important to know the perfect squares when determining the consecutive whole numbers for a square root?

• They help in simplifying the square root.

• They provide a range for the square root.

• They are always greater than the square root.

• They are always less than the square root.

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