# Square Root of 31 — Calculation and Simplification

In math, the square root of 31 is the number that, when multiplied by itself, equals that value. For example, the square root of 31 is 5.5678 because 5.5678 multiplied by itself is 31.

Square root of 31 = **5.5678**

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

The number below

the radix is the **radicand**

## Is 31 a Perfect Square Root?

No. The square root of 31 is not an integer, hence √31 isn't a perfect square.

Previous perfect square root is: 25

Next perfect square root is: 36

## The Prime Factors of 31 are:

**31** is a prime number. It has only two factors: 1 and 31

## How Do You Simplify the Square Root of 31 in Radical Form?

The main point of simplification (to the simplest radical form of 31) is as follows: getting the number 31 inside the radical sign √ as low as possible.

31 is already simplified (prime number).

## Is the Square Root of 31 Rational or Irrational?

Since 31 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 31. To do this, divide the number 31 by 2. As a result of dividing 31/2, we get |

2 | Next, we need to divide 31 by the result of the previous step (15.5). Calculate the arithmetic mean of this value (2) and the result of step 1 (15.5). 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 |

3 | Next, we need to divide 31 by the result of the previous step (8.75). Calculate the arithmetic mean of this value (3.5429) and the result of step 2 (8.75). 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 31 by the result of the previous step (6.1465). Calculate the arithmetic mean of this value (5.0435) and the result of step 3 (6.1465). 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 31 by the result of the previous step (5.595). Calculate the arithmetic mean of this value (5.5407) and the result of step 4 (5.595). 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 31 by the result of the previous step (5.5679). Calculate the arithmetic mean of this value (5.5676) and the result of step 5 (5.5679). 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: 5.5678 In this case, it took us six steps to find the result. |