Math Shortcut: Squaring Numbers from 30 to 50

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: 472

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, 472 = 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, 472= 2209 

Example 2: 422

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, 422 = 1764

Example 3392

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, 392 = 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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  1. Pingback: Month in Review - May 2015 - Math Tricks for Kids

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