Practice Finding Square Roots of Non-Perfect Squares Using the Long Division Method

Introduction

This worksheet provides structured, step-by-step practice for finding square roots of non-perfect square numbers using the long division method. It is designed to help learners understand how decimal extensions naturally arise during the process.

What Makes Non-Perfect Squares Different

Unlike perfect squares, non-perfect square numbers do not have exact whole-number square roots.

Their square roots result in decimals that extend indefinitely. This worksheet focuses on building a clear understanding of how those decimal values are generated systematically using the long division method.

The Long Division Method for Square Roots

The long division method provides a reliable, step-by-step technique for calculating square roots of any number.

By grouping digits into pairs and extending the number with decimal places, learners can progressively refine the square root to the desired level of accuracy.

Step-by-Step Interactive Practice

Each problem is presented in a clear long division layout, closely mirroring the traditional pen-and-paper method.

Dedicated input boxes guide learners to enter intermediate values and the final result in the correct sequence.

This guided structure reinforces correct procedural flow and helps prevent common mistakes.

Decimal Precision Control

Since non-perfect square roots result in decimal values, this worksheet allows you to control how precise the final answer should be.

Using the Decimal Places up to option, you can choose to calculate the square root up to:

• 2 decimal places
• 3 decimal places
• 4 decimal places

This flexibility makes the worksheet suitable for different accuracy requirements and learning levels.

Solution Support

Each problem includes a Solution link.

Clicking this link opens the Square Root Calculator Using Long Division, which displays the complete working steps for that exact non-perfect square in a clear, long division format.

Skills Developed Through This Worksheet

• Accurate application of the long division method for square roots
• Understanding of decimal expansion in non-perfect squares
• Improved precision and attention to calculation detail
• Confidence handling irrational square root values

Online, Interactive, and Self-Checking

This worksheet works entirely online in the browser.

As learners enter values at each step, the system validates the inputs automatically, reinforcing correct application of the method and clarifying how decimal extensions are formed.