The square source of the number 138 is the turning back of squaring the number 11.7473 or increasing the number 11.7473 to the second power (11.74732). Come undo squaring, we take the square root.

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Square root of 138 = **11.7473**

## Is 138 a Perfect Square Root?

No. The square root of 138 is not an integer, for this reason √138 isn"t a perfect square.

Previous perfect square source is: 121

Next perfect square root is: 144

## How carry out You simplify the Square root of 138 in Radical Form?

The main point of simplification (to the simplest radical kind of 138) is as follows: acquiring the number 138 within the radical authorize √ as low as possible.

138 is currently simplified (have no pair prime factors).

## Is the Square source of 138 rational or Irrational?

Since 138 isn"t a perfect square (it"s square source will have an infinite number of decimals), **it is one irrational number**.

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

StepSequencing1 | In step 1, we have to make our first guess about the value of the square root of 138. To carry out this, division the number 138 by 2. As a result of splitting 138/2, we acquire |

2 | Next, we must divide 138 by the an outcome of the previous action (69).138/69 = Calculate the arithmetic mean of this value (2) and the an outcome of action 1 (69).(69 + 2)/2 = Calculate the error by individually the previous worth from the new guess.|35.5 - 69| = 33.533.5 > 0.001 Repeat this action again together the margin the error is greater than than 0.001 |

3 | Next, we have to divide 138 by the an outcome of the previous action (35.5).138/35.5 = Calculate the arithmetic median of this value (3.8873) and the result of step 2 (35.5).(35.5 + 3.8873)/2 = Calculate the error by individually the previous worth from the brand-new guess.|19.6937 - 35.5| = 15.806315.8063 > 0.001 Repeat this action again as the margin the error is higher than than 0.001 |

4 | Next, we have to divide 138 by the result of the previous step (19.6937).138/19.6937 = Calculate the arithmetic average of this value (7.0073) and also the an outcome of action 3 (19.6937).(19.6937 + 7.0073)/2 = Calculate the error by individually the previous value from the new guess.|13.3505 - 19.6937| = 6.34326.3432 > 0.001 Repeat this step again as the margin the error is higher than 보다 0.001 |

5 | Next, we must divide 138 by the an outcome of the previous step (13.3505).138/13.3505 = Calculate the arithmetic typical of this value (10.3367) and also the an outcome of action 4 (13.3505).(13.3505 + 10.3367)/2 = Calculate the error by individually the previous value from the new guess.|11.8436 - 13.3505| = 1.50691.5069 > 0.001 Repeat this step again together the margin the error is better than than 0.001 |

6 | Next, we should divide 138 by the an outcome of the previous action (11.8436).138/11.8436 = Calculate the arithmetic mean of this worth (11.6519) and also the result of step 5 (11.8436).(11.8436 + 11.6519)/2 = Repeat this action again together the margin of error is greater than 보다 0.001 |

7 | Next, we should divide 138 through the result of the previous action (11.7478).138/11.7478 = Calculate the arithmetic mean of this worth (11.7469) and the an outcome of action 6 (11.7478).(11.7478 + 11.7469)/2 = Calculate the error by subtracting the previous value from the new guess.|11.7474 - 11.7478| = 0.00040.0004 |

Result | ✅ We found the result: 11.7474 In this case, that took united state seven procedures to discover the result. |