In the previous post, we have learned an interesting **math shortcut on squaring numbers from 50 to 70**. Before we explain why the shortcut works, we first continue this series by learning a shortcut on squaring numbers from 30 to 50. Notice that the steps are almost similar.

**Example 1: **47^{2}

Step 1: First, consider how far is 47 from 50 (the base). This means that we want 50 – 47 = 3.

Step 2: Subtract 3 from 25. This gives us 23. This gives us 2 as the thousands and 3 as the hundreds digit of the product. That is, 47^{2} = 23xx where xx are the tens and ones digits.

Note: The number 25 comes from squaring the tens digit of 50 (the base).

Step 3: To get xx, we square 3, the number we subtracted in Step 2. This gives us 9. Since xx represents a 2-digit number, we add 0 to make it 09.

Therefore, 47^{2}= 2209

**Example 2: **42^{2}

Step 1: How far is 42 from 50? It’s 8.

Step 2: We subtract 8 from 25 which results to 17. So, our number is 17xx where xx are the tens and the ones digit.

Step 3: To get xx, we square 8. This gives us 64.

Therefore, 42^{2} = 1764

**Example 3**: 39^{2}

Step 1: How far is 39 away from 50? It’s 11.

Step 2: We subtract 11 from 25. This gives us 14xx where xx are the tens and the ones digit of the final answer.

Step 3: We square 11 to get xx. However, the square of 11 is 121. So, xx = 21 and we add 1 to 14. So, the thousands and the hundreds digit as 15.

Therefore, 39^{2} = 1521

In the next post, we are going to discuss why this trick and the trick in the previous post work.

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