Sure, let's break down the solution step by step.
### Part (i): Find the square root of 260 by division method.
First, we approximate the square root of 260. The closest perfect square less than or equal to 260 is 256, which is [tex]\(16^2\)[/tex]. Thus, the integer part of the square root of 260 is 16.
### Part (ii): What is the remainder left in this process?
To find the remainder, we calculate how much more 260 is compared to the square of 16. The square of 16 is:
[tex]\[ 16^2 = 256 \][/tex]
The remainder is therefore:
[tex]\[ 260 - 256 = 4 \][/tex]
### Part (iii): Subtract the remainder from 260. Is the difference a perfect square?
Subtract the remainder from 260:
[tex]\[ 260 - 4 = 256 \][/tex]
Now we check if 256 is a perfect square. Since [tex]\(16^2 = 256\)[/tex], we can see that 256 is indeed a perfect square.
### Summary:
(i) The square root of 260 by division method is approximately 16.
(ii) The remainder left in this process is 4.
(iii) Subtracting the remainder from 260 gives us 256, which is a perfect square (since [tex]\(16^2 = 256\)[/tex]).
Hence, the results are:
- The approximate square root of 260 is 16.
- The remainder when comparing 260 to the square of 16 is 4.
- Subtracting this remainder from 260 results in 256, which is a perfect square.
