Find the square root of 2.56 and 7.29 using the long division method.

i) 2.56

Step 1: Group the digits in pairs from the decimal point. For 2.56, the pairs are 2 and 56.

Step 2: Find the largest integer whose square is less than or equal to the first pair (2). This is 1 ($1^2 = 1$). Write 1 as the quotient and subtract 1 from 2.

Step 3: Bring down the next pair (56) and place the decimal point in the quotient. The new dividend is 156. Double the current quotient (1) to get 2. Find a digit 'x' such that $2x \times x \le 156$. Here, $26 \times 6 = 156$.

$$\begin{array}{r} 1.6 \\[-3pt] 1 \overline{\smash{)} 2.56} \\[-3pt] -1 \phantom{.00} \\[-3pt] \hline 26 \overline{\smash{)} 156} \\[-3pt] -156 \\[-3pt] \hline 0 \end{array}$$

The square root of 2.56 is $\boxed{\text{1.6}}$.

ii) 7.29

Step 1: Group the digits in pairs from the decimal point. For 7.29, the pairs are 7 and 29.

Step 2: Find the largest integer whose square is less than or equal to the first pair (7). This is 2 ($2^2 = 4$). Write 2 as the quotient and subtract 4 from 7.

Step 3: Bring down the next pair (29) and place the decimal point in the quotient. The new dividend is 329. Double the current quotient (2) to get 4. Find a digit 'x' such that $4x \times x \le 329$. Here, $47 \times 7 = 329$.

$$\begin{array}{r} 2.7 \\[-3pt] 2 \overline{\smash{)} 7.29} \\[-3pt] -4 \phantom{.00} \\[-3pt] \hline 47 \overline{\smash{)} 329} \\[-3pt] -329 \\[-3pt] \hline 0 \end{array}$$

The square root of 7.29 is $\boxed{\text{2.7}}$.

iii) 51.84

Step 1: Group the digits in pairs from the decimal point. For 51.84, the pairs are 51 and 84.

Step 2: Find the largest integer whose square is less than or equal to the first pair (51). This is 7 ($7^2 = 49$). Write 7 as the quotient and subtract 49 from 51.

Step 3: Bring down the next pair (84) and place the decimal point in the quotient. The new dividend is 284. Double the current quotient (7) to get 14. Find a digit 'x' such that $14x \times x \le 284$. Here, $142 \times 2 = 284$.

$$\begin{array}{r} 7.2 \\[-3pt] 7 \overline{\smash{)} 51.84} \\[-3pt] -49 \phantom{.00} \\[-3pt] \hline 142 \overline{\smash{)} 284} \\[-3pt] -284 \\[-3pt] \hline 0 \end{array}$$

The square root of 51.84 is $\boxed{\text{7.2}}$.

v) 31.36

Step 1: Group the digits in pairs from the decimal point. For 31.36, the pairs are 31 and 36.

Step 2: Find the largest integer whose square is less than or equal to the first pair (31). This is 5 ($5^2 = 25$). Write 5 as the quotient and subtract 25 from 31.

Step 3: Bring down the next pair (36) and place the decimal point in the quotient. The new dividend is 636. Double the current quotient (5) to get 10. Find a digit 'x' such that $10x \times x \le 636$. Here, $106 \times 6 = 636$.

$$\begin{array}{r} 5.6 \\[-3pt] 5 \overline{\smash{)} 31.36} \\[-3pt] -25 \phantom{.00} \\[-3pt] \hline 106 \overline{\smash{)} 636} \\[-3pt] -636 \\[-3pt] \hline 0 \end{array}$$

The square root of 31.36 is $\boxed{\text{5.6}}$.