1. **State the problem:** Find the square root of 1444 using the division method. 2. **Explain the division method:** This method involves grouping the digits of the number in pairs from right to left and finding the largest number whose square is less than or equal to the first group. 3. **Step 1:** Group the digits of 1444 as (14)(44). 4. **Step 2:** Find the largest number whose square is less than or equal to 14. That number is 3 because $3^2=9$ and $4^2=16$ which is greater than 14. 5. **Step 3:** Subtract $9$ from $14$ to get $5$, then bring down the next pair (44) to make $544$. 6. **Step 4:** Double the current root (3) to get 6. Find a digit $x$ such that $6x \times x \leq 544$. 7. **Step 5:** Try $x=8$: $68 \times 8 = 544$, which fits exactly. 8. **Step 6:** Append 8 to the root, making it 38. The remainder is 0, so the square root is 38. **Final answer:** The square root of 1444 is $38$.