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.

One thought on “Math Shortcut: Squaring Numbers from 50 to 70

  1. Pingback: Math Shortcut: Squaring Numbers from 30 to 50

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