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 3: 392
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
Math Shortcut: Squaring Numbers from 50 to 70
We have already learned how to square numbers from 80 to 100. In this post, we are going to show a shortcut on squaring numbers from 50 to 70. Here are example and the steps.
Example 1: 522
Step 1: Consider how far is 52 from 50. The answer is 2.
Step 2: Add 2 to 25. This gives us 27, 2 is the thousands and 7 the hundreds digit. This gives us 27xx where xx are the tens and ones digits.
Note: The number 25 comes from squaring the tens digit which is 5. I will explain this in the next post.
Step 3: To get xx, we square the ones digit of the given which is 2. This gives us 4. Since we only have 1 digit, we put 0 before 4, giving the value of xx as 04.
Therefore, 522= 2704
Example 2: 582
Step 1: How far is 58 from 50? It’s 8.
Step 2: We add 8 to 25 giving us 33. So, our number is 33xx where xx are the tens and the ones digits.
Step 3: To get xx, we square 8. This gives us 64.
Therefore, 582= 3364
Example 3: 642
Step 1: How far is 64 away from 50? It’s 14.
Step 2: We add 14 to 25. This gives us 39xx where xx are the tens and the ones digit of the final answer.
Step 3: We square 14 to get xx. But the answer here is 196. So, xx = 96 and we add 1 to 39.
Therefore, 642= 4096
Now, try other numbers between 50 and 70 and manually check if the trick still works. A more challenging task would be to find out why the trick works.
In the next post, we will discuss why the trick works.