Here we will show you two ways of finding the unit digit of the square of 57357. First, we will define what the unit digit of the square of 57357 means. Next, we will find the unit digit of the square of 57357 using the Rule Method, and then we will find the unit digit of the square of 57357 using the Math Method.
The last digit (one digit) of the product you get when you multiply 57357 by itself is the unit digit of the square of 57357.
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 57357 depends on 7, because that is the last digit in 57357. 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 57357 is 7, therefore Rule F applies, and the unit digit of the square of 57357 is 9.
Unit digit of the square of 57357 = 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 57357 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 57357 = 9
Of course, instead of using either of the methods above, you can multiply 57357 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 57357. We did that below to double-check that our answer is correct:
57357 × 57357 = 3289825449
Unit digit of 3289825449 is 9.
Unit digit of the square of 57357 = 9
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