Squaring any number ending with "25"

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Here’s a simple method to square any number ending with 25:

Step 1: Start by squaring the last two digits, which are 25. The square of 25 is always 625, so the last part of the result will always end with 625.
Step 2: Look at the digits before the last two digits of the given number.
     If this part is an odd number, consider 5 as the middle part of the result.
     If it’s an even numbe, take 0 as the middle part.
Step 3: Find the square of the remaining digits (ignoring the last two). Add the half of the remaining number (disregard any remainders) to this square. This will form the first part of the result.

Find (225)2


(225)2 = (2)2 + (2/2) | (0 or 5) | (25)2
= 4 + 1 | 0 | 625
= 50625

Step 1:  Start by squaring the last two digits, which are 25.
The square of 25 is 625. This will form the last part of the result.
Step 2:  Look at the remaining digit (2), which is the number formed after removing the last two digits.
Since 2 is an even number, the middle part of the result will be 0.
Step 3:  Square the remaining digit (2) and add its half (ignore remainders).
The square of 2 is 4, and half of 2 is 1. Adding them gives 4 + 1 = 5. This is the first part of the result.
Conclusion: Combining all parts, (225)2 = 50625.

Find (525)2


(525)2 = (5)2 + (5/2) | (0 or 5) | (25)2
= 25 + 2.5 | 5 | 625
= 275625

Step 1:  Start by squaring the last two digits, which are 25.
The square of 25 is 625. This will form the last part of the result.
Step 2:  Look at the remaining digit (5), which is the number formed after removing the last two digits.
Since 5 is an odd number, the middle part of the result will be 5.
Step 3:  Square the remaining digit (5) and add its half (ignore remainders).
The square of 5 is 25, and half of 5 is 2.5. Adding them gives 25 + 2.5 = 27.5. This is the first part of the result.
Conclusion: Combining all parts, (525)2 = 275625.

Find (99525)2


(99525)2 = (995)2 + (995/2) | (0 or 5) | (25)2
= 990025 + 497.5 | 0 | 625
= 990025497625

Step 1:  Start by squaring the last two digits, which are 25.
The square of 25 is 625. This will form the last part of the result.
Step 2:  Look at the remaining digits (995), which is the number formed after removing the last two digits.
Since 995 is odd, the middle part of the result will be 0.
Step 3:  Square the remaining digits (995) and add half of it (ignore remainders).
The square of 995 is 990025, and half of 995 is 497.5. Adding them gives 990025 + 497.5.
Conclusion: Combining all parts, (99525)2 = 990025497625.

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