8th Grade Evaluating Square & Cube Roots Worksheet | Fractions Decimals

A worksheet on evaluating expressions involving square and cube roots. Detailed solutions are included.

Take your students’ radical skills to the next level with this comprehensive Evaluating Square and Cube Roots Worksheet!

Whether you need a rigorous classroom activity, a structured homework assignment, or a reliable assessment, this resource is designed to challenge and support Key Stage 3, Key Stage 4, and GCSE Maths students as they master perfect squares and perfect cubes.

Teachers love that this practice page moves beyond basic whole numbers. It features a wide variety of problem types that truly test student understanding—including fractions, decimals, negative numbers, and multi-step order of operations (BIDMAS)!

What’s Included in This Resource?

• Student Practice Worksheet: Featuring 5 deeply structured, multi-part maths problems.
• Complete, Step-by-Step Answer Key: Four pages showing the exact mathematical breakdown and working out for every single problem. Perfect for easy marking, student self-assessment, or hassle-free cover lessons!

Skills Covered & Problem Breakdown:

• Section 1: Evaluating Basic Roots – Practise finding the square and cube roots of integers, fractions, decimals, and negative numbers (e.g., square root of 81, cube root of 0.027).
• Section 2: Multi-Step Expressions (BIDMAS) – Applying the order of operations to expressions containing radicals, nested roots, fractions, and negative indices.
• Section 3: Solving Radical Equations – Finding the value of “x” in equations involving multiple nested square and cube roots.
• Sections 4 & 5: Algebraic Substitutions & Laws of Indices – Evaluating complex variables and working with base numbers to solve exponential root equations.

Curriculum and Exam Board Alignment:

• UK National Curriculum (KS3/KS4): Recognise and use relationships between operations, including inverse operations (e.g., roots and powers); use integer powers and associated roots.
• GCSE Maths (9-1) Foundation & Higher: Core powers and roots topics across all major exam boards (AQA, Edexcel, OCR).