# What is the Square Root of 630?

The square root of the number 630 is the reverse of squaring the number 25.0998 or raising the number 25.0998 to the second power (25.0998^{2}). To undo squaring, we take the square root.

Square root of 630 = **25.0998**

The symbol √ is called**radix**, or **radical sign**

The number below

the radix is the **radicand**

## Is 630 a Perfect Square Root?

No. The square root of 630 is not an integer, hence √630 isn't a perfect square.

Previous perfect square root is: 625

Next perfect square root is: 676

## The Prime Factors of 630 are:

2 × 3 × 3 × 5 × 7

## How Do You Simplify the Square Root of 630 in Radical Form?

The main point of simplification (to the simplest radical form of 630) is as follows: getting the number 630 inside the radical sign √ as low as possible.

630 = 2 × 3 × 3 × 5 × 7 = 370

Therefore, the answer is **3**70.

## Is the Square Root of 630 Rational or Irrational?

Since 630 isn't a perfect square (it's square root will have an infinite number of decimals), **it is an irrational number**.

## The Babylonian (or Heron’s) Method (Step-By-Step)

Step | Sequencing |
---|---|

1 | In step 1, we need to make our first guess about the value of the square root of 630. To do this, divide the number 630 by 2. As a result of dividing 630/2, we get |

2 | Next, we need to divide 630 by the result of the previous step (315). Calculate the arithmetic mean of this value (2) and the result of step 1 (315). Calculate the error by subtracting the previous value from the new guess. Repeat this step again as the margin of error is greater than than 0.001 |

3 | Next, we need to divide 630 by the result of the previous step (158.5). Calculate the arithmetic mean of this value (3.9748) and the result of step 2 (158.5). Calculate the error by subtracting the previous value from the new guess. Repeat this step again as the margin of error is greater than than 0.001 |

4 | Next, we need to divide 630 by the result of the previous step (81.2374). Calculate the arithmetic mean of this value (7.755) and the result of step 3 (81.2374). Calculate the error by subtracting the previous value from the new guess. Repeat this step again as the margin of error is greater than than 0.001 |

5 | Next, we need to divide 630 by the result of the previous step (44.4962). Calculate the arithmetic mean of this value (14.1585) and the result of step 4 (44.4962). Calculate the error by subtracting the previous value from the new guess. Repeat this step again as the margin of error is greater than than 0.001 |

6 | Next, we need to divide 630 by the result of the previous step (29.3274). Calculate the arithmetic mean of this value (21.4816) and the result of step 5 (29.3274). Calculate the error by subtracting the previous value from the new guess. Repeat this step again as the margin of error is greater than than 0.001 |

7 | Next, we need to divide 630 by the result of the previous step (25.4045). Calculate the arithmetic mean of this value (24.7988) and the result of step 6 (25.4045). Calculate the error by subtracting the previous value from the new guess. Repeat this step again as the margin of error is greater than than 0.001 |

8 | Next, we need to divide 630 by the result of the previous step (25.1017). Calculate the arithmetic mean of this value (25.0979) and the result of step 7 (25.1017). Calculate the error by subtracting the previous value from the new guess. Repeat this step again as the margin of error is greater than than 0.001 |

9 | Next, we need to divide 630 by the result of the previous step (25.0998). Calculate the arithmetic mean of this value (25.0998) and the result of step 8 (25.0998). Calculate the error by subtracting the previous value from the new guess. Stop the iterations as the margin of error is less than 0.001 |

Result | ✅ We found the result: 25.0998 In this case, it took us nine steps to find the result. |