As you should know from your high school algebra course, the square root y of a number x is such that y2 = x. By multiplying the value y by itself, we get the value x. For instance, 6.3246 the square root of 40 because 6.32462 = 6.3246×6.3246 = 40.

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Square root of 40 = **6.3246**

## Is 40 a Perfect Square Root?

No. The square root of 40 is not an integer, hence √40 isn”t a perfect square.

Previous perfect square root is: 36

Next perfect square root is: 49

## How Do You Simplify the Square Root of 40 in Radical Form?

The main point of simplification (to the simplest radical form of 40) is as follows: getting the number 40 inside the radical sign √ as low as possible.

40= 2 × 2 × 2 × 5= 210

Therefore, the answer is **2**10.

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## Is the Square Root of 40 Rational or Irrational?

Since 40 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)

StepSequencing1 |
In step 1, we need to make our first guess about the value of the square root of 40. To do this, divide the number 40 by 2. See more: Sandisk Extreme Plus Vs Samsung Evo Plus, The Best Microsd Cards For 2021 As a result of dividing 40/2, we get |

2 |
Next, we need to divide 40 by the result of the previous step (20).40/20 = Calculate the arithmetic mean of this value (2) and the result of step 1 (20).(20 + 2)/2 = Calculate the error by subtracting the previous value from the new guess.|11 – 20| = 99 > 0.001 Repeat this step again as the margin of error is greater than than 0.001 |

3 |
Next, we need to divide 40 by the result of the previous step (11).40/11 = Calculate the arithmetic mean of this value (3.6364) and the result of step 2 (11).(11 + 3.6364)/2 = Calculate the error by subtracting the previous value from the new guess.|7.3182 – 11| = 3.68183.6818 > 0.001 Repeat this step again as the margin of error is greater than than 0.001 |

4 |
Next, we need to divide 40 by the result of the previous step (7.3182).40/7.3182 = Calculate the arithmetic mean of this value (5.4658) and the result of step 3 (7.3182).(7.3182 + 5.4658)/2 = Calculate the error by subtracting the previous value from the new guess.|6.392 – 7.3182| = 0.92620.9262 > 0.001 Repeat this step again as the margin of error is greater than than 0.001 |

5 |
Next, we need to divide 40 by the result of the previous step (6.392).40/6.392 = Calculate the arithmetic mean of this value (6.2578) and the result of step 4 (6.392).(6.392 + 6.2578)/2 = Calculate the error by subtracting the previous value from the new guess.|6.3249 – 6.392| = 0.06710.0671 > 0.001 Repeat this step again as the margin of error is greater than than 0.001 |

6 |
Next, we need to divide 40 by the result of the previous step (6.3249).40/6.3249 = Calculate the arithmetic mean of this value (6.3242) and the result of step 5 (6.3249).(6.3249 + 6.3242)/2 = Calculate the error by subtracting the previous value from the new guess.|6.3246 – 6.3249| = 0.00030.0003 |

Result | ✅ We found the result: 6.3246 In this case, it took us six steps to find the result. |