Number Sense: Squaring Numbers Ending in 0, 5

Welcome to Mathnasium’s Maths Tricks series. Today we are squaring numbers ending in 0 or 5 by observing patterns and applying our number sense.

To square a number, we multiply it by itself. Sometimes, this multiplication might be difficult to compute, but let’s observe a few patterns that might help us out — see if you and your child can spot them!

902 = 8,100

1102 = 12,100

452 = 2,025

1152 = 13,225

Did you notice that the square of a number ending in 0, such as 90, ends in 00? How about that the beginning of the final answer is the square of the digits in front of 0 in the original number? In the case of 90, 92 = 81.

Did you also notice that the square of a number ending in 5, such as 45, ends in 25? And that the beginning of the final answer is equal to the digits in front of the 5 multiplied by those same digits increased by 1? The square of 45 begins with the digits 20 because 4 multiplied by (4+1) is equal to 4×5 = 20. And this happens all the time!

Follow the examples below to observe more patterns and use them to find the square of each number.

Example 1: Find 1202.

Step 1: Identify the number-sense pattern for squaring numbers.

Since 120 ends with a 0, we turn to the first number-sense trick.

Step 2: Write down two 0s for the end of the final answer.

_____ 00.

Step 3: Square the digits before the 0.

We square the digits 12: 122 = 12 x 12 = 144.

Step 4: Put the answer to Step 3 in front of the 00 in the final answer.

144 00.

Answer: 120 squared is equal to 14,400.

Example 2: Find 1252.

Step 1: Identify the number-sense pattern for squaring numbers.

Since 125 ends with a 5, we turn to the second number-sense trick.

Step 2: Write down 25 for the end of the final answer.

_____ 25.

Step 3: Increase the digits in front of the 5 by 1.

We increase the digits 12 by 1: 12 + 1 = 13.

Step 4: Multiply the original digits in front of the 5 by the digits from Step 3.

We multiply 12 x 13 = 156.

Step 5: Put the answer to Step 4 in front of the 25 in the final answer.

156 25.

Answer: 125 squared is equal to 15,625.

Now, with this strategy, you are ready to square numbers ending in 0 or 5 using the mental maths and number sense. Click here for more practice problems, then check your answers here.