Find the least number which must be subtracted from each of the following numbers so that the resulting number is a perfect square. Also, find the square root of the perfect square so obtained. i) 402

i) 402

Step 1: Find the largest perfect square less than 402 using the long division method.

$$\begin{array}{r} 20 \\[-3pt] 2 \overline{\smash{)} 402} \\[-3pt] -4 \phantom{00} \\[-3pt] \hline 40 \overline{\smash{)} 02} \\[-3pt] -00 \\[-3pt] \hline 2 \end{array}$$

The remainder is 2. This means $20^2 = 400$.

Step 2: The least number to be subtracted is the remainder.

$$402 - 400 = 2$$

Step 3: The square root of the perfect square obtained is 20.
The least number to be subtracted is $\boxed{\text{2}}$, and the square root of the perfect square is $\boxed{\text{20}}$.

ii) 1989

Step 1: Find the largest perfect square less than 1989 using the long division method.

$$\begin{array}{r} 44 \\[-3pt] 4 \overline{\smash{)} 1989} \\[-3pt] -16 \phantom{00} \\[-3pt] \hline 84 \overline{\smash{)} 389} \\[-3pt] -336 \\[-3pt] \hline 53 \end{array}$$

The remainder is 53. This means $44^2 = 1936$.

Step 2: The least number to be subtracted is the remainder.

$$1989 - 1936 = 53$$

Step 3: The square root of the perfect square obtained is 44.
The least number to be subtracted is $\boxed{\text{53}}$, and the square root of the perfect square is $\boxed{\text{44}}$.

iii) 3250

Step 1: Find the largest perfect square less than 3250 using the long division method.

$$\begin{array}{r} 57 \\[-3pt] 5 \overline{\smash{)} 3250} \\[-3pt] -25 \phantom{00} \\[-3pt] \hline 107 \overline{\smash{)} 750} \\[-3pt] -749 \\[-3pt] \hline 1 \end{array}$$

The remainder is 1. This means $57^2 = 3249$.

Step 2: The least number to be subtracted is the remainder.

$$3250 - 3249 = 1$$

Step 3: The square root of the perfect square obtained is 57.
The least number to be subtracted is $\boxed{\text{1}}$, and the square root of the perfect square is $\boxed{\text{57}}$.

iv) 825

Step 1: Find the largest perfect square less than 825 using the long division method.

$$\begin{array}{r} 28 \\[-3pt] 2 \overline{\smash{)} 825} \\[-3pt] -4 \phantom{00} \\[-3pt] \hline 48 \overline{\smash{)} 425} \\[-3pt] -384 \\[-3pt] \hline 41 \end{array}$$

The remainder is 41. This means $28^2 = 784$.

Step 2: The least number to be subtracted is the remainder.

$$825 - 784 = 41$$

Step 3: The square root of the perfect square obtained is 28.
The least number to be subtracted is $\boxed{\text{41}}$, and the square root of the perfect square is $\boxed{\text{28}}$.

v) 4000

Step 1: Find the largest perfect square less than 4000 using the long division method.

$$\begin{array}{r} 63 \\[-3pt] 6 \overline{\smash{)} 4000} \\[-3pt] -36 \phantom{00} \\[-3pt] \hline 123 \overline{\smash{)} 400} \\[-3pt] -369 \\[-3pt] \hline 31 \end{array}$$

The remainder is 31. This means $63^2 = 3969$.

Step 2: The least number to be subtracted is the remainder.

$$4000 - 3969 = 31$$

Step 3: The square root of the perfect square obtained is 63.
The least number to be subtracted is $\boxed{\text{31}}$, and the square root of the perfect square is $\boxed{\text{63}}$.