Unit digit of the square of 10007

Here we will show you two ways of finding the unit digit of the square of 10007. First, we will define what the unit digit of the square of 10007 means. Next, we will find the unit digit of the square of 10007 using the Rule Method, and then we will find the unit digit of the square of 10007 using the Math Method.

The last digit (one digit) of the product you get when you multiply 10007 by itself is the unit digit of the square of 10007.

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 10007 depends on 7, because that is the last digit in 10007. 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 10007 is 7, therefore Rule F applies, and the unit digit of the square of 10007 is 9.

Unit digit of the square of 10007 = 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 10007 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 10007 = 9

Of course, instead of using either of the methods above, you can multiply 10007 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 10007. We did that below to double-check that our answer is correct:

10007 × 10007 = 100140049
Unit digit of 100140049 is 9.
Unit digit of the square of 10007 = 9

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