1. **Stating the problem:** Find the square root of 97344 using the division (long division) method. 2. **Step 1:** Pair the digits of 97344 from right to left: (9)(73)(44). 3. **Step 2:** Find the largest number whose square is less than or equal to the first group 9. That number is 3, since $3^2 = 9$. 4. **Step 3:** Subtract $3^2 = 9$ from 9 to get remainder 0, bring down the next pair 73 to get 073. 5. **Step 4:** Double the divisor 3 to get 6, write it as 6_. Find a digit $x$ such that $6x \times x$ is less than or equal to 73. - Try $x=1$: $61 \times 1 = 61 \leq 73$. - Try $x=2$: $62 \times 2 = 124 > 73$, so $x=1$. 6. **Step 5:** Subtract $61$ from $73$ to get remainder $12$, bring down the next pair $44$ to get $1244$. 7. **Step 6:** Double the current quotient (31), ignoring the last digit to get 62_, then find $x$ such that $62x \times x \leq 1244$. - Try $x=1$: $621 \times 1 = 621 \leq 1244$. - Try $x=2$: $622 \times 2 = 1244 \leq 1244$. - Try $x=3$: $623 \times 3 = 1869 > 1244$, so $x=2$. 8. **Step 7:** Subtract $1244$ from $1244$ to get remainder $0$. 9. **Step 8:** Since remainder is 0 and no more pairs are left, the square root is the quotient formed: $312$. **Final answer:** The square root of 97344 is $312$.