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Free online tool that helps you find the square root of a given number (x).

Square root

One of the most common methods to calculate a square root is the long division method. Here are the steps to calculate a square root using the long division method:

- Write the number whose square root you want to find.
- Pair the digits of the number starting from the right. If there are an odd number of digits, then the leftmost digit will form a pair with a zero.
- Starting from the leftmost pair, find the largest number whose square is less than or equal to the pair. This will be the first digit of the square root.
- Subtract the product of the digit found in step 3 and itself from the pair, and bring down the next pair of digits (if any).
- Double the digit found in step 3, and write it as the divisor next to the remainder obtained in step 4.
- Divide the new dividend by the new divisor to obtain the next digit of the square root.
- Repeat steps 4 to 6 until you obtain the desired number of digits of the square root.

Here's an example to illustrate the process:

Let's calculate the square root of 784.

- Write the number: 784
- Pair the digits: 7|84
- Find the largest number whose square is less than or equal to 7. The largest number whose square is less than or equal to 7 is 2, so the first digit of the square root is 2.
- Subtract: 7 - 4 = 3. Bring down the next pair of digits: 38.
- Double: 2 x 2 = 4. Write it as the divisor next to the remainder: 3|38, 4.
- Divide: 34 ÷ 4 = 8. Write 8 as the next digit of the square root.
- Repeat:
- New dividend: 38. Bring down the next pair of digits: 384.
- Double: 2 x 2 = 4. Write it as the divisor next to the remainder: 38|4, 4.
- Divide: 344 ÷ 44 = 7. Write 7 as the next digit of the square root.

Therefore, the square root of 784 is 28.

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, the square root of a non-negative number x is a non-negative number y such that y times y equals x.

For example, the square root of 25 is 5 because 5 times 5 equals 25. Similarly, the square root of 4 is 2 because 2 times 2 equals 4.

The symbol used to represent the square root operation is √, and the number inside the symbol is called the radicand. For example, √25 means the square root of 25.

√1 | 1 |
---|---|

√2 | 1.414214 |

√3 | 1.732051 |

√4 | 2 |

√5 | 2.236068 |

√6 | 2.44949 |

√7 | 2.645751 |

√8 | 2.828427 |

√9 | 3 |

√10 | 3.162278 |

√11 | 3.316625 |

√12 | 3.464102 |

√13 | 3.605551 |

√14 | 3.741657 |

√15 | 3.872983 |

√16 | 4 |

√17 | 4.123106 |

√18 | 4.242641 |

√19 | 4.358899 |

√20 | 4.472136 |