What is the square root of 10000 by the long division method?

The square root of 10000, calculated using the long division method, is 100.

Here's a breakdown of how the long division method is applied to find the square root of 10000:

Group the digits: Start by grouping the digits of the number (10000) in pairs, starting from the right. In this case, we have 1 00 00.
Find the largest square less than or equal to the leftmost group: The leftmost group is "1". The largest perfect square less than or equal to 1 is 1 itself (1 x 1 = 1). Write "1" as the quotient and subtract 1 from the leftmost group.
```
    1
√1 00 00
- 1
-------
    0
```
Bring down the next pair of digits: Bring down the next pair "00" to the right of the remainder. Now we have 000, or simply 00.
```
    1
√1 00 00
- 1
-------
    0 00
```
Double the quotient and find the next digit: Double the current quotient (1), which gives you 2. Now we need to find a digit (let's call it 'x') such that (2x) * x is less than or equal to 00. Since we have just 00 as the next number, x=0 works the best.
```
    1 0
√1 00 00
- 1
-------
    0 00
 -  0
 ------
    00
```
Bring down the next pair of digits: Bring down the next pair of digits "00".
```
    1 0
√1 00 00
- 1
-------
    0 00
 -  0
 ------
    00 00
```
Double the quotient and find the next digit: Double the current quotient (10), which gives you 20. Now we need to find a digit (let's call it 'x') such that (20x) * x is less than or equal to 0000. x=0 also works here.
```
    1 0 0
√1 00 00
- 1
-------
    0 00
 -  0
 ------
    00 00
 -  0
 -------
    0
```
Final Answer: Since the remainder is 0, the square root of 10000 is 100.

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