Easiest method of Squaring any number @kidsknowledgepoint

Squaring a Number Using the Vedic Math Vertical and Crosswise Method

Vedic mathematics offers several efficient techniques for mathematical calculations, one of which is the vertical and crosswise method for squaring numbers. This technique simplifies the squaring process by breaking it down into manageable steps involving vertical and crosswise multiplication. Here's how you can use this method:

Steps for Squaring a Number Using Vertical and Crosswise Multiplication

1. Identify the Number and Split It

Consider the number to be squared as a two-digit number split into its tens and units place. For example, to square 42, split it into 40 (tens place) and 2 (units place).

2. Apply Vertical and Crosswise Multiplication

The vertical and crosswise method uses the identity $(a + b)^2 = a^2 + 2ab + b^2$, where:

• $a$ is the tens digit (in this case, 40)
• $b$ is the units digit (in this case, 2)

3. Perform the Calculations

• Vertical Multiplication:
  • Square the tens digit: $a^2$
  • Square the units digit: $b^2$
• Crosswise Multiplication:
  • Multiply the tens and units digits, then double the product: $2ab$

4. Combine the Results

Add the results from the vertical and crosswise multiplications to get the final squared value.

Example: Squaring 42

1. Split the Number: 42 = 40 + 2
2. Apply the Formula:
   • $a = 40$, $b = 2$
   • $(a + b)^2 = a^2 + 2ab + b^2$
3. Perform the Calculations:
   • Vertical:
     • $a^2 = 40^2 = 1600$
     • $b^2 = 2^2 = 4$
   • Crosswise:
     • $2ab = 2 \times 40 \times 2 = 160$
4. Combine the Results:
   • $a^2 + 2ab + b^2 = 1600 + 160 + 4 = 1764$

Thus, $42^2 = 1764$.

Conclusion

The vertical and crosswise method from Vedic math provides a clear and efficient way to square numbers. By breaking the process into vertical and crosswise multiplications, this technique makes complex calculations more manageable and enhances mental math skills. Practicing this method can help you quickly and accurately square numbers.