Mastering Surds
Mathematics
Year 9
5 questions
~10 mins
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About This Worksheet
A worksheet covering Surds for Year 9 students.
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Mastering Surds
Subject: MathematicsGrade: Year 9
Name:
Date:
Untitled Worksheet
Grade Year 9
A
Introduction
Read the key concepts below before attempting the questions.
1.
A surd is an expression involving a square root that cannot be simplified to a rational number. Recall that √n represents the square root of n.
[2 marks]2.
Simplify √50.
[1 mark]3.
Express √8 as a simplified surd.
[1 mark]4.
If √x = 3√2, find the value of x.
[2 marks]5.
Simplify √72 + √18.
[2 marks]B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Simplify √200.
[1 mark]2.
Calculate the value of √50 + √8.
[2 marks]3.
Express √125 as a simplified surd.
[1 mark]4.
If √x = 4√3, find the value of x.
[2 marks]5.
Simplify √18 - √8.
[2 marks]C
Reasoning and Problem-Solving
Use your understanding of surds to solve these problems.
1.
Express the sum of √32 and √18 in simplest surd form.
[2 marks]2.
If √x = 7√3, determine x and explain your reasoning.
[3 marks]3.
Simplify the expression √50 × √8.
[2 marks]4.
The sum of two surds is 10, and one of them is 3√2. Find the other surd.
[2 marks]5.
A shape's area is given by √50 × √18. Calculate the area in simplest surd form.
[3 marks]D
Challenge / Real-World Application
Tackle these challenging problems to deepen your understanding.
1.
A ladder is placed against a wall, reaching a height of √80 meters. If the ladder's length is √200 meters, find the horizontal distance from the bottom of the ladder to the wall.
[4 marks]2.
In a garden, the diagonal of a rectangular plot measures √125 meters, and one side is √45 meters. Find the length of the other side.
[3 marks]Quick Actions
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet