√a × √b: Error Analysis & Misconceptions
Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on multiplying surds of the form √a × √b, designed to address common misconceptions and develop procedural mastery for GCSE Foundation students.
Worksheet Preview
Full preview • 11 questions
√a × √b: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Foundation
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Answer the following questions to practice multiplying surds. Show your working clearly in the grid spaces provided.
1.
Calculate √3 × √12 and simplify your answer.
[2 marks]2.
Simplify √5 × √20.
[2 marks]3.
Evaluate √2 × √8.
[2 marks]4.
Simplify √7 × √3.
[2 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems involving surds. Explain your reasoning clearly.
1.
If √a × √b = √(ab), explain why √18 × √2 = √36 and find its simplified form.
[3 marks]2.
A rectangular garden has sides √50 meters and √18 meters. Find the area in simplest surd form and evaluate it approximately.
[4 marks]C
Real-world Applications
Apply your understanding of multiplying surds in these real-world contexts.
1.
A construction project requires a concrete slab with an area of √50 m². If the length and width are both √10 meters, verify this matches the area and explain the calculation.
[3 marks]D
Challenge & Extension
Attempt these more advanced problems to extend your understanding.
1.
Prove that √12 × √27 = √324 and evaluate the result.
[3 marks]2.
Construct a diagram on the grid to represent √32 × √8 as a rectangle with sides √32 and √8. Find its area in simplified surd form.
[3 marks]E
Mixed Review & Error Analysis
Identify the mistake in each of these common errors and correct it.
1.
Student's solution: √6 × √3 = √(6×3) = √18. Is this correct? If not, explain and correct the mistake.
[2 marks]2.
A student simplifies √45 × √5 as √(45+5) = √50. Identify the mistake and provide the correct answer.
[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