To find the square root of 5776 using the long division method, follow these steps:

Step 1: Group the digits in pairs from right to left

5776 can be grouped as:

$57\text{ | }76$

Step 2: Find the largest number whose square is less than or equal to the first group (57)

• The square root of 57 falls between $7^2 = 49$ and $8^2 = 64$.
• The largest number is 7 because $7^2 = 49$.

So, place 7 as the first digit of the square root. The first part of the quotient is 7.

Step 3: Subtract $49$ from $57$

$57 - 49 = 8$ Now, bring down the next pair of digits (76), so we have 876.

Step 4: Double the first quotient and use it as a trial divisor

• Double 7, which gives $2 \times 7 = 14$.
• Write it on the left as part of the new divisor.

Now, find a digit $d$ such that $14d \times d$ is less than or equal to 876.

Step 5: Find $d$

• Try $d = 6$, so $146 \times 6 = 876$.

So, the second digit of the square root is 6.

Step 6: Conclusion

The square root of 5776 is 76.

Would you like more details or have any questions? Here are some related questions for practice:

1. What is the square root of 7225 using the long division method?
2. Find the square root of 3844 using the long division method.
3. What is the square root of 1444?
4. How do you apply the long division method to non-perfect squares?
5. Calculate the square root of 5184 using long division.

Tip: For quicker results with square roots of large numbers, first estimate by finding the nearest perfect square.