b) Let’s take a number 260 .
(i) Find the square root of 260 by division method.
(ii) What is the remainder left in this process?
(iii) Subtract the remainder from 260 . Is the difference a perfect square?

b) Given Number: 260

(i) Find the square root of 260 by the division method.

1. Pair the Digits:
   • Start from the decimal point and pair the digits in twos: 2 | 60
2. Find the Largest Square ≤ First Pair (2):
   • The largest integer whose square is ≤ 2 is 1 (since ).
   • Quotient so far: 1
   • Remainder:
3. Bring Down the Next Pair (60):
   • Combine the remainder with the next pair: (remainder) becomes 160.
4. Double the Current Quotient and Find the Next Digit:
   • Double the current quotient (1): .
   • Find a digit x such that .
     • Testing x = 6:
     • Next digit: 6
   • Quotient so far: 16
   • Remainder:
5. (Optional) Continue for Decimal Precision:
   • If you need more decimal places, continue the process by bringing down pairs of zeros and repeating the steps. For simplicity, we’ll stop here.
   Approximate Square Root: (to the nearest integer)

(ii) What is the remainder left in this process?

• Remainder: 4

(iii) Subtract the remainder from 260. Is the difference a perfect square?

• Calculate the Difference:
• Check if 256 is a Perfect Square:
  Yes, 256 is a perfect square since .

Summary:

• (i) The square root of 260 is 16 with a remainder.
• (ii) The remainder is 4.
• (iii) Subtracting the remainder from 260 gives 256, which is a perfect square ( ).