Question bank: Irrational Numbers

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Question 1:

Easy

Which of the numbers below is rational?

Irrational Numbers

Basic Calculus

Question 2:

Medium

An architect is designing a garden in the shape of a regular hexagon, a polygon with six equal sides and equal internal angles. He decides that each side of the hexagon will have a length of 4 meters, totaling 24 meters of perimeter. However, he needs to calculate the length of the diagonals of the hexagon to determine the position of the luminaires. a) What is the length of a diagonal of the hexagon? b) Based on the result of the first question, justify whether this length is or is not a rational number. c) Explain how irrational numbers can arise in this scenario and provide examples.

Irrational Numbers

Question 3:

Medium

Irrational Numbers

Question 4:

Medium

During a geometry class, a 9th-grade class studied polygons and triangles and learned that some line segments have lengths that cannot be expressed as rational numbers. To explore this concept, consider a square ABCD with sides of length 1 unit. a) Calculate the measure of the diagonal of this square using the Pythagorean theorem. b) Verify if the measure of the diagonal found is a rational or irrational number. Justify your answer. c) Give an example of a triangle whose height cannot be expressed by a rational number, considering the length of each side as a unit. Justify your choice with a mathematical argument.

Irrational Numbers

Question 5:

Easy

Irrational Numbers

IARA TIP

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