Square root calculator
The square root of a number is a value that when multiplied by itself gives the original number. It is denoted by the symbol √. For example, the square root of 25 is 5, because 5 x 5 = 25. The square root of a negative number is not a real number, but can be represented by imaginary numbers.
To find the square root of a number, you can use a calculator or use the long division method. Here is the long division method:
- Start by grouping the digits of the number into pairs, starting from the decimal point and working backwards. If there is only one digit left over, add a zero to make a pair.
- Find the largest perfect square that is less than or equal to the leftmost pair of digits. Write the square root of that number above the pair.
- Subtract the product of the square root and itself from the leftmost pair of digits, and write the remainder next to the next digit in the dividend.
- Bring down the next pair of digits and add it to the remainder to form a new dividend.
- Double the square root and write it next to the previous one. Then, find the largest digit to fill in the blank such that the product of the new two-digit number and the digit is less than or equal to the new dividend.
- Subtract the product of the new two-digit number and the digit from the new dividend, and write the remainder next to the next digit in the dividend.
- Repeat steps 5 and 6 until all the digits have been used. The final answer is the square root of the original number.