√a × √b: Problem Solving & Reasoning
Mathematics
Grade 6
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on multiplying surds of the form √a × √b, designed to develop procedural skills, problem solving, and real-world application for Grade 6 students.
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√a × √b: Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Fluency & Practice
Calculate the following. Show your working in the grid spaces provided.
1.
Simplify √36 × √49.
[2 marks]2.
Calculate √25 × √16.
[2 marks]3.
Evaluate √81 × √9.
[2 marks]4.
Simplify √64 × √25.
[2 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems. Show your reasoning clearly.
1.
A square garden has an area of √144 m². What is the length of each side of the garden? Explain your reasoning.
[3 marks]2.
A builder is laying tiles in a rectangular hall. The number of tiles along the length is √49, and along the width is √36. Find the total number of tiles used and explain how you calculated it.
[3 marks]3.
An area of √81 square meters is covered in a square patch. What is the length of one side? Show your work.
[2 marks]4.
A container has a capacity of √100 liters. If it is filled to full capacity, how many liters are in the container? Explain.
[3 marks]C
Real-world Applications
Apply your knowledge to solve these real-world problems involving surds.
1.
A carpenter measures the diagonal of a square table as √50 cm. Find the length of each side of the table.
[2 marks]2.
A swimming pool has a length of √64 meters and a width of √36 meters. What is the area of the pool? Show your work.
[3 marks]D
Challenge & Extension
Tackle these more challenging problems that extend your understanding.
1.
Simplify √200 × √50 and express your answer in simplest surd form.
[3 marks]2.
If √a × √b = √c, and a = 18, b = 32, find c. Then verify by calculation.
[3 marks]E
Mixed Review & Error Analysis
Attempt these questions and identify any common mistakes in the solutions.
1.
A student simplifies √36 × √49 as 42. Is this correct? Explain and correct if necessary.
[2 marks]2.
Identify the mistake: Simplify √25 × √16 as 20, then correct it.
[2 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