Pythagorean Theorem & Classify Rational & Irrational Numbers CW

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

How do you find the length of the missing side in a right triangle?

Back

To find the length of the missing side, use the Pythagorean Theorem: a² + b² = c². Rearrange the formula to solve for the missing side.

Front

What are rational numbers?

Back

Rational numbers are numbers that can be expressed as a fraction or ratio of two integers, where the denominator is not zero.

Front

What are irrational numbers?

Back

Irrational numbers are numbers that cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions.

Front

Is 0 a rational number?

Back

Yes, 0 is a rational number because it can be expressed as 0/1.

Front

Is the square root of 2 a rational number?

Back

No, the square root of 2 is an irrational number because it cannot be expressed as a fraction.

Front

What is an example of a rational number?

Back

Examples of rational numbers include 1/2, -3, and 0.75.

Front

What is an example of an irrational number?

Back

Examples of irrational numbers include π (pi) and √3.

Front

If a right triangle has one side of length 3 and another side of length 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5.

Front

What is the relationship between whole numbers and rational numbers?

Back

All whole numbers are rational numbers because they can be expressed as a fraction with a denominator of 1.