Mastering Surds
Mathematics
GCSE Foundation
0 questions
0 views0 downloads
About This Worksheet
A worksheet covering Surds for GCSE Foundation students, focusing on understanding, simplifying, and applying surds in various contexts.
Topics covered:
Worksheet Preview
Full preview • 0 questions
Mastering Surds
Subject: MathematicsGrade: GCSE Foundation
Name:
Date:
Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Review the key concepts related to surds. Remember that surds are irrational roots that cannot be simplified to a rational number unless simplified as a radical expression.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Simplify: √50
[2 marks]2.
Simplify: √18 + √8
[2 marks]3.
Calculate: (√3)^2
[1 mark]4.
Express as a simplified surd: 8√2 / 2
[2 marks]5.
Simplify: √75 × √3
[2 marks]6.
If √x = 3, find the value of x.
[2 marks]7.
Determine whether √12 + √3 is rational or irrational.
[1 mark]8.
Simplify: √200 - √50
[2 marks]9.
Express √45 as a simplified surd.
[2 marks]10.
Calculate: √2 × √8
[2 marks]C
Reasoning and Problem Solving
Use your understanding of surds to solve these questions. Show your working clearly.
1.
Simplify the expression: (√3 + √2)^2
[3 marks]2.
A square has a side length of √7 meters. Find its area.
[3 marks]3.
Express the sum √12 + √3 in the form a√b, where a and b are integers in simplest form.
[3 marks]4.
If √x + √y = 7 and √x - √y = 3, find the value of √x.
[4 marks]5.
A student simplifies √80 to 4√5. Is this correct? Explain your reasoning.
[4 marks]D
Challenge / Real-World Application
Solve these challenging questions involving surds in real-world contexts.
1.
A ladder leans against a wall, forming a 45° angle with the ground. If the length of the ladder is √50 meters, how high does it reach on the wall?
[4 marks]2.
A rectangular garden has a diagonal of length √85 meters and one side of 6 meters. Find the length of the other side.
[4 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
Related Worksheets
Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet