Exploring Rational and Irrational Numbers

The video tutorial explains the difference between rational and irrational numbers, providing examples such as Pi and the square root of non-perfect squares. It describes rational numbers as those that can be expressed as fractions or terminating decimals. Real numbers are introduced as a combination of both rational and irrational numbers. The tutorial also covers how to determine if a number is rational or irrational and provides a method for estimating square roots of non-perfect squares.

What defines an irrational number?

• A number that is a perfect square.

• A number that only contains integers.

• A number that does not end or repeat.

• A number that can be written as a simple fraction.

Which of the following numbers is rational?

• The square root of 13

• The square root of 5

• The square root of 25

• Pi (π)

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

• The square root of 2

• The square root of 13

• 5.2

• Pi (π)

What makes a number rational?

• It is a perfect square.

• It is an integer.

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

• It continues indefinitely without repeating.

What are real numbers composed of?

• Only rational numbers

• Only irrational numbers

• Neither rational nor irrational numbers

• Both rational and irrational numbers

Is 0.25 a rational or irrational number?

• Neither

• Irrational

• Cannot be determined

• Rational

Why is the square root of 12 considered irrational?

• Because it can be written as a fraction

• Because it is a positive number

• Because it is a perfect square

• Because it cannot be expressed as a fraction of two integers

Which of the following is an irrational number?

• 256

• 5.2

• The square root of 12

• 0.25

What is the estimated value of the square root of 58?

• Exactly 8

• Exactly 7

• Between 7 and 8, closer to 8

• Between 7 and 8, closer to 7

Is the square root of 30 closer to 5 or 6?

• Closer to 6

• Exactly 5

• Closer to 5

• Exactly 6