Finding Squares of Numbers Ending in 5

Introduction

This is a simple trick to quickly find the squares of numbers that end in 5. In other words, those numbers whose unit digit (or ones digit) is the number 5. This is just a specific case of the trick Quickly multiply when the unit digits add up to 10

Choose a number

The Trick is...

352 = 1225

The Trick in detail

• Step 1: Ignoring the unit digit 5, take the remaining digits as a number.
• Step 2: Multiply the number by its successor.
• Step 3: Append 25 to the product from Step 2 to get the required square value.

In equation form

The logic of this trick is nothing but

where n is a number ending in 5.

This Trick on Bigger numbers

Let's use the same trick to quickly find the squares of some bigger numbers from the series 115, 125, 135, 145... up to 305.

• Step 1: Ignoring the unit digit 5, take the remaining digits as a number.
• Step 2: Multiply the number by its successor using the trick.†
• Step 3: Append 25 to the product from Step 2 to get the required square value.

Our worksheets

Once you've learnt this trick, please do visit Squares and Cubes worksheet pages and put your learnings into practice.