Mental Math Tricks: Square Two Digit Numbers in Seconds

Do you ever find yourself struggling to calculate the square of a two-digit number? It can be a tedious task, especially if you're in a hurry or don't have a calculator handy. But fear not! There's a simple and efficient mental math trick that can help you square any two-digit number in seconds. Let's explore this technique and see how it works.

The Trick

The trick relies on breaking down the two-digit number into its tens and units digits and applying some basic arithmetic operations. Here's how it goes:

1. Identify the tens digit: Let's take the number 23 as an example. The tens digit is 2.
2. Square the tens digit: Square the tens digit (2 in our example), which gives us 4.
3. Double the product of the tens and units digit: Multiply the tens digit (2) by the units digit (3) and double the result. 2 * 3 = 6, and doubling it gives us 12.
4. Square the units digit: Square the units digit (3), which gives us 9.
5. Combine the results: Combine the results from steps 2, 3, and 4 by concatenating them: 4 12 9.
6. Adjust for carry-over: If the middle number (12 in our example) is greater than or equal to 10, carry over the tens digit (1) to the leftmost number (4) and add it to the result. So, 4 12 9 becomes 5 2 9.

Therefore, the square of 23 is 529.

Example: Squaring 37

1. Tens digit: 3
2. Square of tens digit: 3 * 3 = 9
3. Double the product of tens and units digit: 3 * 7 = 21, doubled is 42
4. Square of units digit: 7 * 7 = 49
5. Combine the results: 9 42 49
6. Adjust for carry-over: 9 42 49 becomes 13 69

Hence, the square of 37 is 1369.

Why Does This Work?

This trick is based on the algebraic expansion of (a + b)², where 'a' represents the tens digit and 'b' represents the units digit. Expanding the expression, we get:

(a + b)² = a² + 2ab + b²

The steps in the mental math trick correspond to the terms in this expansion:

• a²: Square of the tens digit
• 2ab: Double the product of the tens and units digit
• b²: Square of the units digit

By combining these terms and adjusting for carry-over, we arrive at the correct square of the two-digit number.

Practice Makes Perfect

This mental math trick might seem a bit tricky at first, but with practice, you'll be able to square two-digit numbers quickly and effortlessly. Start by practicing with simple numbers and gradually increase the complexity. You'll be surprised how quickly you can master this technique and impress your friends with your mental math skills.