Squaring Numbers: CRISS-CROSS or Rainbow Method

Squaring any number mentally using the Criss-cross or Rainbow method is actually very fast and interesting to calculate.

Squaring a 2-digit Number using CRISS-CROSS method

Step-1:  Square the unit’s (right) digit. Write a partial answer and carry, if any. This gives the right most figure of the answer.

Step-2:  Multiply both the digit of the number to be squared and then double (multiply by 2) the product. Add the carry, if any. Write again a partial answer and carry, if any.

Step-3:  Square the ten’s (left) digit and add carry, if any. Write the complete result. This gives the left figure(s) of the answer.

Let’s say you want to square 58.

First, square the one’s digit that is 8. Square of 8 is 64. Write 4 and carry 6.

Then, multiply the two digits of the number which are 5 and 8. So, 5 times 8 is 40. Now, double this product: 40×2=80. Add carry 6 to get 86. Write 6 and carry 8.

Finally, square the ten’s digit that is 5. Square of 5 is 25. Add carry 8 to get 33.

So, our final answer is 3364.

67² =?

1.   Square of 7 is 49. Write down 9 and carry 4.

2.   Then, 6 times 7 is 42. And, 42×2 = 84. Add carry 4 to get 88. Write 8 and carry 8.

3.   Finally, square of 6 is 36. And 36 plus carry 8 is 44. Write down 44.

So, the final answer is 4489.

73² =?

Square of 3 is 9. Write 9. -> 9

7 times 3 is 21. And, 21×2=42. Write 2 and carry 4. -> 29

Square of 7 is 49. And 49 plus carry 4 is 53. Write down 53. -> 5329

So, 73² =5329

Squaring a 3-digit Number using CRISS-CROSS method

Step-1:  Square the unit’s (right) digit. Write a partial answer and carry, if any. This gives the right most figure of the answer.

Step-2:  Multiply the middle digit by the right digit of the number and then double (multiply by 2) the product. Add the carry, if any. Write again the units digit of the answer and carry, if any.

Step-3:  Multiply the left digit with the right digit of the number and double the product. Add this to the square of the middle digit and then add the carry. Write the units digit of the answer and carry, if any.

Step-4:  Multiply the left digit with the middle digit of the number and double the product. Add carry. Write the units digit of the answer and carry, if any.

Step-5:  Square the left digit and add carry, if any. Write the complete result. This gives the left figure(s) of the answer.

Example, 789² =?

9² = 81. Write 1 carry 8 à 1

(9×8) × 2 = 144 + carry 8 = 152. Write 2, carry 15 à 21

(9×7) × 2 + 8² = 126 + 64 = 190 + carry 15 = 205, write 5, carry 20 à 521

(8×7) × 2 = 112+carry 20 = 132. Write 2, carry 13 à 2521

7² = 49 + carry 13 = 62. Write 62 à 622521

So, our final answer is 622521.