Unit digit of the square of 321

Here we will show you two ways of finding the unit digit of the square of 321. First, we will define what the unit digit of the square of 321 means. Next, we will find the unit digit of the square of 321 using the Rule Method, and then we will find the unit digit of the square of 321 using the Math Method.

The last digit (one digit) of the product you get when you multiply 321 by itself is the unit digit of the square of 321.

Rule Method
The unit digit of any square will never be 2, 3, 7, or 8. It can be only 0, 1, 4, 5, 6, or 9. Furthermore, the unit digit of the square of a number depends on its units digit. In other words, the unit digit of the square of 321 depends on 1, because that is the last digit in 321. Here are the rules:

Rule A) If the unit digit of a number is 0, then the unit digit of the square of that number is 0.

Rule B) If the unit digit of a number is 1 or 9, then the unit digit of the square of that number is 1.

Rule C) If the unit digit of a number is 2 or 8, then the unit digit of the square of that number is 4.

Rule D) If the unit digit of a number is 5, then the unit digit of the square of that number is 5.

Rule E) If the unit digit of a number is 4 or 6, then the unit digit of the square of that number is 6.

Rule F) If the unit digit of a number is 3 or 7, then the unit digit of the square of that number is 9.

The unit digit of 321 is 1, therefore Rule B applies, and the unit digit of the square of 321 is 1.

Unit digit of the square of 321 = 1

Math Method
The unit digit of the square of a number depends on its units digit with this method too. Here you multiply the unit digit of the number by itself, and then look at the unit digit of that product. Again, the unit digit of 321 is 1, so you multiply 1 by itself, and then look at the unit digit to get the answer once again:

1 × 1 = 1
Unit digit of 1 is 1.
Unit digit of the square of 321 = 1

Of course, instead of using either of the methods above, you can multiply 321 by itself if you have the time or a calculator, and then identify the unit digit to get the answer to the unit digit of the square of 321. We did that below to double-check that our answer is correct:

321 × 321 = 103041
Unit digit of 103041 is 1.
Unit digit of the square of 321 = 1

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