√a × √b: Challenge & Extension
Mathematics
Year 9
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focusing on simplifying expressions involving √a × √b, designed to deepen understanding and promote problem-solving skills.
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√a × √b: Challenge & Extension
Subject: MathematicsGrade: Year 9
Name:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Simplify √50 × √8.
[2 marks]2.
Calculate √18 × √2.
[2 marks]3.
Simplify √72 × √3.
[2 marks]4.
Evaluate √200 × √50.
[2 marks]B
Problem Solving & Reasoning
Answer all questions clearly, showing your reasoning and working.
1.
Express √108 × √75 in simplest radical form and explain each step.
[4 marks]2.
If √x × √y = 12 and √x = 3√2, find the value of y.
[3 marks]3.
Prove that √a × √b = √(ab) by starting from the prime factorizations of a and b.
[4 marks]C
Real-world Applications
Solve the problems below with clear working.
1.
A carpenter needs to cut a piece of wood that measures √32 meters in length, and another that measures √18 meters. Find the total length if combined, simplified as a surd.
[3 marks]D
Challenge & Extension
Attempt these advanced problems. Show full working.
1.
Simplify √75 × √12 and express your answer in simplest radical form.
[3 marks]2.
Given √x × √y = √36 and √x = 2√3, find y and justify your answer.
[3 marks]E
Mixed Review & Error Analysis
Answer the following questions. For error analysis, identify the mistake and correct it.
1.
Simplify √80 × √2. A student claims the answer is 10√2. Is this correct? Explain your reasoning.
[2 marks]2.
Identify and correct the mistake in simplifying √45 × √20 as 15√3.
[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