# What is the Exact Square Root of 36?

As you should know from your high school algebra course, the square root `y` of a number `x` is such that `y ^{2}` =

`x`. By multiplying the value

`y`by itself, we get the value

`x`. For instance, 6 the square root of 36 because 6

^{2}= 6×6 = 36.

Square root of 36 = **6**

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

The number below

the radix is the **radicand**

## Is 36 a Perfect Square Root?

Yes. The square root of 36 is 6. Since 6 is a whole number, 36 is a perfect square.

Previous perfect square root is: 25

Next perfect square root is: 49

## The Prime Factors of 36 are:

2 × 2 × 3 × 3

## How Do You Simplify the Square Root of 36 in Radical Form?

The main point of simplification (to the simplest radical form of 36) is as follows: getting the number 36 inside the radical sign √ as low as possible.

36 = 2 × 2 × 3 × 3 = 6

Therefore, the answer is **6**.

## Is the Square Root of 36 Rational or Irrational?

Since 36 is a perfect square (it's square root will have no decimals), **it is a rational 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 36. To do this, divide the number 36 by 2. As a result of dividing 36/2, we get |

2 | Next, we need to divide 36 by the result of the previous step (18). Calculate the arithmetic mean of this value (2) and the result of step 1 (18). 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 36 by the result of the previous step (10). Calculate the arithmetic mean of this value (3.6) and the result of step 2 (10). 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 36 by the result of the previous step (6.8). Calculate the arithmetic mean of this value (5.2941) and the result of step 3 (6.8). 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 36 by the result of the previous step (6.0471). Calculate the arithmetic mean of this value (5.9533) and the result of step 4 (6.0471). 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 36 by the result of the previous step (6.0002). Calculate the arithmetic mean of this value (5.9998) and the result of step 5 (6.0002). 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: 6 In this case, it took us six steps to find the result. |