Exact Values: Real-world Applications in Engineering
Mathematics
Grade 7
14 questions
~28 mins
1 views0 downloads
About This Worksheet
This worksheet explores the concept of exact square root values within engineering contexts. Students will practice calculating, reasoning, and applying these values to real-world scenarios.
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Exact Values: Real-world Applications in Engineering
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Calculate the exact value of each square root. Show your working in the grid spaces provided.
1.
Calculate the exact value of √49.
[1 mark]2.
Find the value of √81.
[1 mark]3.
Evaluate √144.
[1 mark]4.
Determine the value of √25.
[1 mark]B
Problem Solving & Reasoning
Solve the following multi-step problems. Show detailed reasoning in the grid areas.
1.
An engineer is designing a square panel with an area of 64 square meters. What is the length of each side?
[2 marks]2.
A bridge segment has a length that is the square root of 81 meters. If the length is doubled, what is the new length?
[2 marks]C
Real-world Applications
Apply your understanding of exact square roots to engineering scenarios.
1.
An engineer needs a square metal sheet with an area of 100 square meters. What should be the length of each side? Explain how you determine the answer.
[3 marks]2.
A rectangular component has a length of √49 meters and a width of √36 meters. Calculate its area.
[3 marks]D
Challenge & Extension
Tackle these advanced problems involving exact square roots and their applications.
1.
A square panel has an area of √121 square meters. If the side length is increased by √2 meters, what is the new area? Show all steps.
[4 marks]2.
Find the value of √(50) + √(18). Simplify your answer.
[2 marks]E
Mixed Review
Answer these variety of questions to reinforce your understanding of exact square roots.
1.
Calculate the exact value of √36.
[1 mark]2.
Construct a square on the grid with a side length of √25.
[2 marks]F
Error Analysis
Review the common mistakes and identify the errors in the following calculations.
1.
A student calculated √49 as 6. Identify and correct the mistake.
[2 marks]2.
A student simplified √50 as 5√2, but wrote the answer as 10√2. Explain the mistake and correct it.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet