Here we will show you two ways of finding the unit digit of the square of 52803. First, we will define what the unit digit of the square of 52803 means. Next, we will find the unit digit of the square of 52803 using the Rule Method, and then we will find the unit digit of the square of 52803 using the Math Method.
The last digit (one digit) of the product you get when you multiply 52803 by itself is the unit digit of the square of 52803.
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 52803 depends on 3, because that is the last digit in 52803. 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 52803 is 3, therefore Rule F applies, and the unit digit of the square of 52803 is 9.
Unit digit of the square of 52803 = 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 52803 is 3, so you multiply 3 by itself, and then look at the unit digit to get the answer once again:
3 × 3 = 9
Unit digit of 9 is 9.
Unit digit of the square of 52803 = 9
Of course, instead of using either of the methods above, you can multiply 52803 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 52803. We did that below to double-check that our answer is correct:
52803 × 52803 = 2788156809
Unit digit of 2788156809 is 9.
Unit digit of the square of 52803 = 9
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