a^(1/n): Problem Solving & Reasoning
Mathematics
GCSE Higher
15 questions
~30 mins
1 views0 downloads
About This Worksheet
This worksheet explores the concept of fractional indices, focusing on a^(1/n). It includes procedural questions, problem-solving tasks, real-world contexts, and extension challenges suitable for GCSE Higher students.
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Full preview • 15 questions
a^(1/n): Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the value of 8^(1/3).
[2 marks]2.
Simplify (16)^(1/4).
[2 marks]3.
Evaluate 81^(1/4).
[2 marks]B
Targeted Practice
Answer all questions. Show your working clearly on the grid.
1.
Express 125^(1/3) as a simplified radical or integer.
[2 marks]2.
Calculate (32)^(1/5).
[2 marks]3.
Simplify the expression (256)^(1/8).
[2 marks]4.
Evaluate 625^(1/4).
[2 marks]C
Problem Solving & Reasoning
Answer all questions carefully, showing detailed working in the grid.
1.
If a = 64, find the value of a^(1/3) and explain what this represents geometrically.
[3 marks]2.
Solve for x: (x^2)^(1/4) = 3. Show all steps.
[3 marks]3.
A ladder leans against a wall, forming a right-angled triangle. If the length of the ladder is 125 units and the height from ground to top of the ladder is 25 units, estimate the horizontal distance from the wall to the base of the ladder using roots.
[4 marks]D
Real-world Applications
Answer all questions, providing reasoning in your working.
1.
A certain chemical reaction involves the square root of the concentration of a substance. If the concentration is 16 units, what is its square root? How does this relate to fractional indices?
[3 marks]E
Challenge & Extension
Attempt these more difficult questions. Show detailed working.
1.
Given that a^(1/3) = 2, find the value of a^(2/3).
[3 marks]2.
If (x^3)^(1/2) = 8, what is the value of x? Provide the reasoning.
[3 marks]F
Mixed Review & Error Analysis
Answer all questions. For the error analysis, identify the mistake and correct it.
1.
A student incorrectly states that (81)^(1/2) = 9. Is this right? If not, correct the statement and explain why.
[2 marks]2.
Simplify (125)^(2/3) and explain your steps.
[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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet