The division method (also known as the long division method) for finding the square root of a number involves these steps:

Step-by-Step: Finding the Square Root of 256

1. Group the digits in pairs: Group the digits of 256 starting from the right. Since 256 is a three-digit number, group it as (2)(56).

2. Find the largest square: Find the largest square number less than or equal to the leftmost group. In this case, for the group "2", the largest square is $1^2 = 1$. Subtract 1 from 2 to get the remainder:
   $2 - 1 = 1$.

3. Bring down the next pair: Bring down the next pair of digits, "56". Now we have 156.

4. Double the quotient: The current quotient is 1, so double it to get 2. Write this as the first part of the divisor.

5. Find the next digit of the quotient: Find a digit $x$ such that when you append $x$ to the divisor (i.e., 2 becomes 2x) and multiply by $x$, the result is as close as possible to 156 but not greater. In this case, $x = 6$, because $26 \times 6 = 156$.

6. Subtract and bring down the next pair: Subtract 156 from 156 to get 0, and there are no more digits to bring down.

The quotient we get is 16, so the square root of 256 is 16.

Conclusion

Thus, $\sqrt{256} = 16$.

Do you have any questions or need further clarification on this process?

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5 Related Questions:

1. What is the square root of 144 using the division method?
2. How do you find the square root of a decimal number using the division method?
3. Can the division method be used for non-perfect squares?
4. What is the general formula for the division method in finding square roots?
5. How does the division method compare to other methods for finding square roots?

Tip: The division method is most useful when you need a precise square root without using a calculator for larger numbers.