1. **Problem Statement:** Check if 8836 is a perfect square using the Vedic Square Root method. 2. **Vedic Square Root Method Overview:** - The method involves splitting the number into parts and using known squares and differences. - For a 4-digit number $abcd$, split into two parts: the first two digits $ab$ and the last two digits $cd$. - Find the largest square less than or equal to $ab$ and use it to estimate the root. 3. **Step-by-step for 8836:** - Split 8836 into 88 and 36. - Largest perfect square less than or equal to 88 is $81 = 9^2$. - So, the first digit of the root is 9. - Subtract $81$ from $88$: $88 - 81 = 7$. - Append the last two digits 36 to 7 (as 736). - Double the root found so far (9): $2 \times 9 = 18$. - Find a digit $x$ such that $18x \times x \leq 736$. - Try $x=4$: $184 \times 4 = 736$ exactly. - So, the second digit is 4. 4. **Conclusion:** - The square root of 8836 is $94$. - Since the calculation fits perfectly, 8836 is a perfect square. 5. **Summary:** - Using the Vedic method, we confirmed 8836 is a perfect square with root 94. Final answer: $$\sqrt{8836} = 94$$