Simplifying √n: Error Analysis & Misconceptions
Mathematics
Year 9
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet exploring common errors and misconceptions when simplifying surds, with practice questions spanning procedural mastery to challenging problems. Designed to develop understanding of simplifying √n for Year 9 students.
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Simplifying √n: Error Analysis & Misconceptions
Subject: MathematicsGrade: Year 9
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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 and express the answer in simplest radical form.
[2 marks]2.
Calculate √72 and write the simplified form.
[2 marks]3.
Simplify √18 and express as a mixed number if applicable.
[2 marks]4.
Simplify √200 and write your answer with a radical in simplest form.
[2 marks]B
Problem Solving & Reasoning
Answer all questions with clear explanations and show your working.
1.
A rectangular garden has an area of √288 square meters. If one side of the garden is 12 meters, find the length of the other side in simplest radical form.
[3 marks]2.
A ladder leans against a wall, forming a hypotenuse of √50 meters. If the base of the ladder is 5√2 meters from the wall, calculate the height the ladder reaches on the wall.
[3 marks]C
Real-world Applications
Solve these word problems involving surds in context.
1.
A piece of wire is √125 meters long. If it is cut into pieces each measuring 5√5 meters, how many pieces can be cut? Express your answer as a whole number.
[3 marks]2.
A square has an area of √800 square centimeters. Find the length of one side in simplest radical form.
[2 marks]D
Challenge & Extension
Attempt these harder problems to extend your understanding.
1.
Express the sum of √72 and √200 in simplest radical form and simplify completely.
[3 marks]2.
Simplify the expression: (√98 + √50) ÷ √2. Show all your steps.
[3 marks]E
Mixed Review
Answer these questions to review your understanding of simplifying surds.
1.
Identify the mistake in simplifying √80 as 8√2 and correct it.
[2 marks]2.
Simplify √45 and express your answer in simplest radical form.
[2 marks]3.
Simplify √200 and √72. Which is larger?
[3 marks]Quick Actions
What is Remix?
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet