What walk square root mean? by definition, the square root of 149 is the number that, multiply by itself, to produce the given number 149. In this case, the number is 12.2066.

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Square source of 149 = 12.2066


Is 149 a Perfect Square Root?

No. The square root of 149 is no an integer, thus √149 isn"t a perfect square.

Previous perfect square root is: 144

Next perfect square root is: 169


How execute You simplify the Square root of 149 in Radical Form?

The main allude of leveling (to the easiest radical kind of 149) is together follows: acquiring the number 149 inside the radical sign √ as low as possible.

149 is already simplified (prime number).


Is the Square source of 149 rational or Irrational?

Since 149 isn"t a perfect square (it"s square root will have an infinite variety of decimals), it is an irrational number.


The Babylonian (or Heron’s) technique (Step-By-Step)

StepSequencing
1

In action 1, we should make our very first guess about the worth of the square root of 149. To execute this, division the number 149 through 2.

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As a result of dividing 149/2, we acquire the first guess: 74.5

2

Next, we need to divide 149 by the result of the previous step (74.5).149/74.5 = 2

Calculate the arithmetic median of this value (2) and the an outcome of step 1 (74.5).(74.5 + 2)/2 = 38.25 (new guess)

Calculate the error by individually the previous value from the brand-new guess.|38.25 - 74.5| = 36.2536.25 > 0.001

Repeat this step again together the margin that error is better than than 0.001

3

Next, we need to divide 149 by the result of the previous step (38.25).149/38.25 = 3.8954

Calculate the arithmetic mean of this value (3.8954) and the an outcome of step 2 (38.25).(38.25 + 3.8954)/2 = 21.0727 (new guess)

Calculate the error by subtracting the previous value from the new guess.|21.0727 - 38.25| = 17.177317.1773 > 0.001

Repeat this action again as the margin the error is higher than 보다 0.001

4

Next, we must divide 149 by the result of the previous action (21.0727).149/21.0727 = 7.0708

Calculate the arithmetic average of this value (7.0708) and also the result of step 3 (21.0727).(21.0727 + 7.0708)/2 = 14.0718 (new guess)

Calculate the error by subtracting the previous value from the new guess.|14.0718 - 21.0727| = 7.00097.0009 > 0.001

Repeat this action again together the margin the error is higher than 보다 0.001

5

Next, we need to divide 149 through the an outcome of the previous step (14.0718).149/14.0718 = 10.5886

Calculate the arithmetic typical of this worth (10.5886) and also the result of action 4 (14.0718).(14.0718 + 10.5886)/2 = 12.3302 (new guess)

Calculate the error by subtracting the previous worth from the brand-new guess.|12.3302 - 14.0718| = 1.74161.7416 > 0.001

Repeat this step again as the margin of error is higher than than 0.001

6

Next, we should divide 149 by the result of the previous step (12.3302).149/12.3302 = 12.0842

Calculate the arithmetic mean of this value (12.0842) and also the result of step 5 (12.3302).(12.3302 + 12.0842)/2 = 12.2072 (new guess)

Calculate the error by subtracting the previous worth from the new guess.|12.2072 - 12.3302| = 0.1230.123 > 0.001

Repeat this action again together the margin that error is greater than 보다 0.001

7

Next, we need to divide 149 by the result of the previous action (12.2072).149/12.2072 = 12.2059

Calculate the arithmetic average of this worth (12.2059) and the an outcome of action 6 (12.2072).(12.2072 + 12.2059)/2 = 12.2066 (new guess)

Calculate the error by subtracting the previous worth from the brand-new guess.|12.2066 - 12.2072| = 0.00060.0006

Result✅ We uncovered the result: 12.2066 In this case, that took us seven procedures to discover the result.