Unit digit of the square of 407

Here we will show you two ways of finding the unit digit of the square of 407. First, we will define what the unit digit of the square of 407 means. Next, we will find the unit digit of the square of 407 using the Rule Method, and then we will find the unit digit of the square of 407 using the Math Method.

The last digit (one digit) of the product you get when you multiply 407 by itself is the unit digit of the square of 407.

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 407 depends on 7, because that is the last digit in 407. 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 407 is 7, therefore Rule F applies, and the unit digit of the square of 407 is 9.

Unit digit of the square of 407 = 9

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 407 is 7, so you multiply 7 by itself, and then look at the unit digit to get the answer once again:

7 × 7 = 49
Unit digit of 49 is 9.
Unit digit of the square of 407 = 9

Of course, instead of using either of the methods above, you can multiply 407 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 407. We did that below to double-check that our answer is correct:

407 × 407 = 165649
Unit digit of 165649 is 9.
Unit digit of the square of 407 = 9

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