Log inSign up for FREE
Library

Algebra: Unit 3

Last updated 9 months ago
11 questions
1

Unit 3 - Item 1
Which of the following measurements for piece B would be equivalent to (\sqrt{108}) feet long?

Unit 3 – Item 2
Thomas drew the square with the noted side length.
1

What is the area of the shape?

1

Is the area of the shape a rational or irrational number? Explain.

Unit 3 – Item 3
Mr. Johnson’s class is planning to create a new school garden that has the shape of a regular
hexagon (all side lengths are equal) with two flowerbeds inside that are square and an equilateral triangle in shape. The measurement of one side of the square flower bed is marked below. (Image not drawn to scale)

1

If one side of the garden is 2 1/2 the length of one side of the square flower bed, what is the perimeter of the garden?

1

The perimeter of the triangular flower bed can be represented by the following expression: 3^3 \sqrt{64}. What is the length of one side of the triangle?

Unit 3 – Item 4
A garden is in the shape of a square.
Eric wants to plant cabbage, potatoes, and carrots in the garden. The entire garden would have an area of 144 square meters.

1

If the length of one side of each cabbage plot is 4 meters, what is the area of the entire cabbage section?

1

What is the area of the potato section if one side is 2√20 meters?

1

What is the area of the entire carrot section if each section of carrots has an area of 4 square meters?

Unit 3 - Item 5
The city is planning to build a new observation tower that will be open to the public. The construction team has encountered a challenge related to the height of the tower.

1

The lead architect has identified two possible heights for the observation tower: 45 meters and √200 meters.

Explain whether each of these heights is rational or irrational, providing a detailed explanation of the properties that distinguish rational and irrational numbers. Which one is a more reasonable choice?

1

B.) During a city council meeting, someone proposes that the observation tower's height should be expressed as the square root of √225 meters because it's a perfect square. Evaluate this claim
and explain whether the resident's argument is valid or not. Support your response with mathematical reasoning and consider the implications of using a perfect square for the height of
the observation tower.

1

Unit 3 – Item 6
Is \sqrt{25} a rational or an irrational number? Explain.