Find the least number which must be added to 525 and 1750 to make them a perfect square. Also, find the square root of the perfect squares so obtained.

i) 525

Step 1: Find the largest perfect square less than 525 using the long division method.

$$\begin{array}{r} 22 \\[-3pt] 2 \overline{\smash{)} 525} \\[-3pt] -4 \phantom{00} \\[-3pt] \hline 42 \overline{\smash{)} 125} \\[-3pt] -84 \\[-3pt] \hline 41 \end{array}$$

The quotient is 22, and the remainder is 41. This means $22^2 = 484$.

Step 2: The next perfect square is $(22+1)^2 = 23^2 = 529$.

Step 3: The least number to be added is the difference between the next perfect square and the given number.

$$529 - 525 = 4$$

Step 4: The square root of the perfect square obtained is 23.
The least number to be added is $\boxed{\text{4}}$, and the square root of the perfect square is $\boxed{\text{23}}$.

ii) 1750

Step 1: Find the largest perfect square less than 1750 using the long division method.

$$\begin{array}{r} 41 \\[-3pt] 4 \overline{\smash{)} 1750} \\[-3pt] -16 \phantom{00} \\[-3pt] \hline 81 \overline{\smash{)} 150} \\[-3pt] -81 \\[-3pt] \hline 69 \end{array}$$

The quotient is 41, and the remainder is 69. This means $41^2 = 1681$.

Step 2: The next perfect square is $(41+1)^2 = 42^2 = 1764$.

Step 3: The least number to be added is the difference between the next perfect square and the given number.

$$1764 - 1750 = 14$$

Step 4: The square root of the perfect square obtained is 42.
The least number to be added is $\boxed{\text{14}}$, and the square root of the perfect square is $\boxed{\text{42}}$.

iii) 252

Step 1: Find the largest perfect square less than 252 using the long division method.

$$\begin{array}{r} 15 \\[-3pt] 1 \overline{\smash{)} 252} \\[-3pt] -1 \phantom{00} \\[-3pt] \hline 25 \overline{\smash{)} 152} \\[-3pt] -125 \\[-3pt] \hline 27 \end{array}$$

The quotient is 15, and the remainder is 27. This means $15^2 = 225$.

Step 2: The next perfect square is $(15+1)^2 = 16^2 = 256$.

Step 3: The least number to be added is the difference between the next perfect square and the given number.

$$256 - 252 = 4$$

Step 4: The square root of the perfect square obtained is 16.
The least number to be added is $\boxed{\text{4}}$, and the square root of the perfect square is $\boxed{\text{16}}$.

iv) 1825

Step 1: Find the largest perfect square less than 1825 using the long division method.

$$\begin{array}{r} 42 \\[-3pt] 4 \overline{\smash{)} 1825} \\[-3pt] -16 \phantom{00} \\[-3pt] \hline 82 \overline{\smash{)} 225} \\[-3pt] -164 \\[-3pt] \hline 61 \end{array}$$

The quotient is 42, and the remainder is 61. This means $42^2 = 1764$.

Step 2: The next perfect square is $(42+1)^2 = 43^2 = 1849$.

Step 3: The least number to be added is the difference between the next perfect square and the given number.

$$1849 - 1825 = 24$$

Step 4: The square root of the perfect square obtained is 43.
The least number to be added is $\boxed{\text{24}}$, and the square root of the perfect square is $\boxed{\text{43}}$.

v) 6412

Step 1: Find the largest perfect square less than 6412 using the long division method.

$$\begin{array}{r} 80 \\[-3pt] 8 \overline{\smash{)} 6412} \\[-3pt] -64 \phantom{00} \\[-3pt] \hline 160 \overline{\smash{)} 012} \\[-3pt] -000 \\[-3pt] \hline 12 \end{array}$$

The quotient is 80, and the remainder is 12. This means $80^2 = 6400$.

Step 2: The next perfect square is $(80+1)^2 = 81^2 = 6561$.

Step 3: The least number to be added is the difference between the next perfect square and the given number.

$$6561 - 6412 = 149$$

Step 4: The square root of the perfect square obtained is 81.
The least number to be added is $\boxed{\text{149}}$, and the square root of the perfect square is $\boxed{\text{81}}$.