## How to Calculate the Value of the Square Root of 100?

The square root of \(100\) can be found by the various methods which are given below:

- Prime factorization method
- Long division method
- Repeated subtraction method

### Square Root of 100 by Prime Factorization Method:

Prime factorisation method is the easiest way to find the square root of numbers that are perfect squares. Follow the steps below to find the square root of \(100\) using prime factorization:

**Step 1:** Determine the prime factors of \(100\), i.e. \(100 = 10^{2}\)

**Step 2:** Group the equal prime factors of \(100\) together, i.e. \(100 = (10 \times 10)\)

**Step 3:** Pick one factor from each pair and the square root of \(100\) can be written as:

\(\sqrt{100}=\sqrt{(10 \times 10)}\)

\(\Rightarrow\) \(\sqrt{100}=10\)

So, the square root of \(100\) by prime factorization method is \(10\).

### Square Root of 100 by Long Division Method:

The long division method helps to find the square root of numbers that are not perfect squares by hand. Follow the below steps to find the square root of \(100\) by long division method:

**Step 1: **First pair the digits of the given number starting with the unit’s place and place a horizontal bar on top of the pairs to indicate the pairing.

**Step 2: **We will find a number which on multiplication with itself gives a product less than or equal to \(1\). We know that \(1 \times 1 = 1\). Hence, the difference is \(0\) and the quotient is \(1\).

**Step 3: **Now, we have to bring down \(00\) and multiply the quotient by \(2\). This gives us \(2\). Hence, \(2\) is the starting digit of the new divisor.

**Step 4:** \(0\) is placed at the unit’s place of the new divisor because when \(20\) is multiplied by \(0\), we get \(0\). The remainder thus obtained is \(0\).

The steps should look as follows:

Thus the square root of \(100\) by long division method is \(10\).

### Square Root of 100 by Repeated Subtraction Method:

In the repeated subtraction method, we have to repeatedly subtract the given number by consecutive odd numbers until we get the result as zero. The \(n\)th odd number after which the number is reduced to zero is the square root of the given number.

For the given number \(100\), steps for repeated subtraction are:

Step 1 | 100 – 1 | = | 99 |

Step 2 | 99 – 3 | = | 96 |

Step 3 | 96 – 5 | = | 91 |

Step 4 | 91 – 7 | = | 84 |

Step 5 | 84 – 9 | = | 75 |

Step 6 | 75 – 11 | = | 64 |

Step 7 | 64 – 13 | = | 51 |

Step 8 | 51 – 15 | = | 36 |

Step 9 | 36 – 17 | = | 19 |

Step 10 | 19 – 19 | = | 0 |

Hence, the result zero is obtained in the \(10\)th step, this means that the square root of \(100\) by repeated subtraction method is \(10\).