Rational and Irrational Numbers

The video tutorial explains the concepts of real, rational, and irrational numbers. It defines real numbers as those appearing on the number line, and further categorizes them into rational and irrational numbers. Rational numbers can be expressed as fractions with integer numerators and non-zero denominators, and their decimal forms either terminate or repeat. In contrast, irrational numbers cannot be expressed as such fractions, and their decimal forms neither terminate nor repeat. The tutorial provides examples of both rational and irrational numbers, including integers, fractions, and square roots. It also analyzes specific numbers to determine their classification and discusses the rationality of square roots, emphasizing the role of perfect squares.

What is a characteristic of rational numbers?

• They are always negative.

• They cannot be expressed as fractions.

• Their decimal form never repeats.

• They can be expressed as a fraction of two integers.

Which of the following is a rational number?

• Square root of 5

• Pi

• 0.333...

• Square root of 2

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CCSS.8.NS.A.1

Why is the number Pi considered irrational?

• Its decimal form does not terminate or repeat.

• Its decimal form terminates.

• It is a negative number.

• It can be expressed as a fraction.

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CCSS.8.NS.A.1

Which of the following numbers is irrational?

• 0.5

• Square root of 17

• 0.25

• Square root of 16

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CCSS.8.NS.A.1

What makes a decimal number irrational?

• It does not terminate or repeat.

• It is less than zero.

• It terminates.

• It repeats.

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CCSS.8.NS.A.1

How can you determine if the square root of a number is irrational?

• If the number is negative.

• If the number is a perfect square.

• If the number is not a perfect square.

• If the number is even.

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CCSS.6.EE.A.1

Which of the following is a perfect square?

• 17

• 25

• 20

• 18

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CCSS.8.EE.A.2

What is the square root of 81?

• 9

• 8

• 7

• 10

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CCSS.8.NS.A.2

Which of the following numbers is between 4 and 5 and is irrational?

• Square root of 25

• Square root of 20

• Square root of 17

• Square root of 16

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CCSS.8.NS.A.2

What is the decimal approximation of the square root of 17?

• 4.4

• 4.3

• 4.2

• 4.1

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CCSS.8.NS.A.2