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Square and Cube Numbers

Estimating Square Roots WORKSHEET

Suitable for Year groups: Year 7, Year 8
GCSE Tier: Foundation
Targeting grades: 1-3
Prerequisite knowledge: Square numbers and associated roots.
Learning Objective: Distinguish between exact representations of roots and their decimal approximations.

Estimating Square Roots WORKSHEET DESCRIPTION

This worksheet helps students develop confidence in estimating square roots without a calculator.

Section A introduces the concept by asking learners to identify two consecutive integers between which a given square root lies, using inequality notation. This lays the groundwork for understanding square roots numerically.

In Section B, students work with double number lines, a visual scaffold that helps them locate and estimate square roots to one decimal place, supporting learners who benefit from structured visual aids.

Section C builds on this by removing the scaffolding; here, students independently estimate square roots to one decimal place, applying their understanding in a less guided context.

Finally, Section D challenges learners with a variety of applications: completing inequalities, matching square root estimates to calculation results, and solving basic equations that require square root estimation. This section encourages deeper thinking and fluency.
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All worksheets are created by the team of experienced teachers at Cazoom Maths.

Estimating Square Roots Worksheet suitable for Year 7 and Year 8 students

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Frequently Asked Questions

Students should have a solid understanding of square numbers and their associated roots before tackling these estimation activities. This foundation is essential because learners need to recognise perfect squares like 16, 25, and 36 to identify the consecutive integers that non-perfect square roots fall between. Without this prerequisite knowledge, students will struggle to make reasonable estimates and apply the inequality notation effectively.