Understanding Rational and Irrational Numbers

The video tutorial explores the concepts of rational and irrational numbers. It begins by defining rational numbers as those expressible as a ratio of two integers, and irrational numbers as those that cannot be expressed this way. Through examples, it demonstrates that the number 9 is rational, while the square root of 45 is irrational. The tutorial further simplifies expressions to show their rationality or irrationality, concluding with an example of multiplying the principal root of 9 to illustrate rationality.

What is a rational number?

• A number that can be expressed as a ratio of two integers.

• A number that is always negative.

• A number that is always positive.

• A number that cannot be expressed as a ratio of two integers.

Which of the following is a rational number?

• Square root of 2

• Square root of 5

• 9

• Pi

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CCSS.8.NS.A.1

Why is the square root of 45 considered irrational?

• It is a whole number.

• It can be expressed as a ratio of two integers.

• It is a non-perfect square.

• It is a perfect square.

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CCSS.HSN.RN.B.3

What happens when you add a rational number to an irrational number?

• The result is always a whole number.

• The result is always rational.

• The result is always irrational.

• The result is always zero.

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CCSS.HSN.RN.A.2

What is the result of simplifying the expression 3 times the square root of 5 over 3 times the square root of 5?

• 0

• Square root of 5

• 1

• 3

Which of the following expressions is rational?

• Square root of 45

• 3 times the square root of 5

• Square root of 9 times 5

• 1/1

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CCSS.8.EE.A.2

What is the principal root of 9?

• 2

• 3

• 4

• 1

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

How can the number 9 be expressed as a ratio of two integers?

• 9/9

• 9/0

• 9/1

• 9/10

What is the result of 3 times the principal root of 9?

• 12

• 15

• 9

• 6

Which of the following is an example of a rational number?

• Square root of 2

• Pi

• Square root of 3

• 1/1