Mathnasium #MathTricks: Number Sense (Squaring Numbers Part 2)

Welcome to Mathnasium’s Math Tricks, series. Today we are using number sense to square any number.

In an earlier Mathnasium Math Trick we looked at the patterns when squaring numbers ending in 0 or 5. For example, to find 45² we increase the digits in front of the 5 by 1 and multiply the answer by the original digits in front of the 5, (i.e., 5 x 4 = 20). We then write this number with 25 at the end to get a final answer of

But did you know you can use similar steps to find the square of ANY number, using mental math?

To square any number:
1. Subtract the last digit of the number being squared.
2. Add the last digit to the number being squared.
3. Multiply the numbers from Step 1 and Step 2.
4. Square the last digit of the number being squared and add it to the answer from Step 3.

Follow the example below to find the square of the number.

Example: Find 213².

Step 1: Subtract the last digit from the number being squared.

Step 2: Add the last digit to the number being squared.

Step 3: Multiply the numbers from Step 1 and Step 2.

Step 4: Square the last digit of the number being squared and add it to the answer from Step 3.

Answer: 213 squared is equal to 45,369.

Now, with this strategy, you are ready to find the square of any number using mental math. Click here for more practice problems, then check your answers here.

If you missed this, or any of our other Math Tricks videos, check them out on our YouTube channel!