Here we will show you two ways of finding the unit digit of the square of 57407. First, we will define what the unit digit of the square of 57407 means. Next, we will find the unit digit of the square of 57407 using the Rule Method, and then we will find the unit digit of the square of 57407 using the Math Method.
The last digit (one digit) of the product you get when you multiply 57407 by itself is the unit digit of the square of 57407.
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 57407 depends on 7, because that is the last digit in 57407. 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 57407 is 7, therefore Rule F applies, and the unit digit of the square of 57407 is 9.
Unit digit of the square of 57407 = 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 57407 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 57407 = 9
Of course, instead of using either of the methods above, you can multiply 57407 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 57407. We did that below to double-check that our answer is correct:
57407 × 57407 = 3295563649
Unit digit of 3295563649 is 9.
Unit digit of the square of 57407 = 9
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