Square a 3-digit number when the middle number is zero

Recommended Lessons

Not sure where to start? These are the lessons and games we recommend most to students, parents and teachers on Basic-mathematics.com. Each lesson explains the topic in plain language, walks you through worked examples step by step, and ends with practice so you can check your understanding. Pick one below, or use the menu to find lessons on fractions, algebra, geometry, statistics and more.

You can quickly square a 3-digit number when the middle number (number in the tens place) is zero in about 4 seconds by following this trick.

Example #1

(604)2

Step 1

Square 6 and write it down on the left: 62 = 36

36

Step 2

Square 4 and write it down on the right side of 36: 42 = 16

36          16

Notice how we leave a space between 36 and 16. 

Step 3

Multiply 2 by the product of the number in the ones place and the number in the hundreds place. 

2 × 6 × 4 = 48

Step 4

Write 48 between 36 and 16 and you are done.

(604)2 = 364816 

When working on step 2, if after squaring the digit in the ones place you get a number less than 10, just add a zero on the left. Example #2 below shows how to do this!

Example #2

(903)2

Step 1

Square 9 and write it down on the left: 92 = 81 

81

Step 2

Square 3: 32 = 9

Since 9 is smaller than 10, put a zero on the left of it and write everything on the right side of 81.

81          09

Step 3

Multiply 2 by the product of the number in the ones place and the number in the hundreds place. 

2 × 3 × 9 = 54

Step 4

Write 54 between 81 and 09 and you are done.

(903)2 = 815409