Exact Values: Challenge & Extension
Mathematics
Year 9
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet designed to deepen understanding of exact values of square roots, including procedural mastery, reasoning, and real-world applications.
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Exact Values: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Date:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the exact value of √25.
[1 mark]2.
Simplify √48 in its simplest radical form.
[2 marks]3.
Evaluate √81 and express it as an integer.
[1 mark]4.
Express √50 as a simplified radical.
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working in the grid spaces provided.
1.
If √x = 7, find the value of x and explain your reasoning.
[3 marks]2.
Prove that √18 + √8 = 3√2 + 2√2 and simplify the expression.
[3 marks]3.
A square has an area of 50 cm². Find the length of its side in radical form, explaining each step.
[3 marks]C
Real-world Applications
Answer all questions. Show your working clearly.
1.
An engineer designs a square garden with an area of 200 m². Find the length of each side in simplest radical form.
[3 marks]2.
A ladder leans against a wall, forming a right triangle with the ground. If the ladder's length is √80 meters, what is the height it reaches on the wall?
[3 marks]D
Challenge & Extension
Attempt these challenging questions. Show detailed solutions.
1.
Solve for x: √(x + 3) = √x + 1. Explain your reasoning and verify the solution.
[4 marks]2.
Express √200 + √50 in simplest radical form and compare their values.
[3 marks]E
Mixed Review & Error Analysis
Answer all questions. For the error analysis, identify and correct the mistake.
1.
Calculate √36 + √64.
[1 mark]2.
A student incorrectly calculates √50 as 7.1. Identify and explain the mistake, then provide the correct answer.
[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