Unit digit of the square of 105

Here we will show you two ways of finding the unit digit of the square of 105. First, we will define what the unit digit of the square of 105 means. Next, we will find the unit digit of the square of 105 using the Rule Method, and then we will find the unit digit of the square of 105 using the Math Method.

The last digit (one digit) of the product you get when you multiply 105 by itself is the unit digit of the square of 105.

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 105 depends on 5, because that is the last digit in 105. 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 105 is 5, therefore Rule D applies, and the unit digit of the square of 105 is 5.

Unit digit of the square of 105 = 5

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 105 is 5, so you multiply 5 by itself, and then look at the unit digit to get the answer once again:

5 × 5 = 25
Unit digit of 25 is 5.
Unit digit of the square of 105 = 5

Of course, instead of using either of the methods above, you can multiply 105 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 105. We did that below to double-check that our answer is correct:

105 × 105 = 11025
Unit digit of 11025 is 5.
Unit digit of the square of 105 = 5

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