As you should know from her high college algebra course, the square source y of a number x is such the y2 = x. By multiply the worth y by itself, we gain the value x. For instance, 14.4222 the square root of 208 because 14.42222 = 14.4222×14.4222 = 208.

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Square root of 208 = 14.4222

## Is 208 a Perfect Square Root?

No. The square root of 208 is no an integer, for this reason √208 isn"t a perfect square.

Previous perfect square source is: 196

Next perfect square source is: 225

## How do You leveling the Square source of 208 in Radical Form?

The main point of leveling (to the easiest radical kind of 208) is together follows: acquiring the number 208 within the radical authorize √ together low as possible.

208= 2 × 2 × 2 × 2 × 13= 413

Therefore, the prize is 413.

## Is the Square root of 208 rational or Irrational?

Since 208 isn"t a perfect square (it"s square root will have actually an infinite number of decimals), it is one irrational number.

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

StepSequencing
1

In step 1, we must make our very first guess around the worth of the square root of 208. To perform this, divide the number 208 by 2.

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As a result of splitting 208/2, we obtain the very first guess: 104

2

Next, we have to divide 208 by the an outcome of the previous action (104).208/104 = 2

Calculate the arithmetic typical of this value (2) and also the an outcome of action 1 (104).(104 + 2)/2 = 53 (new guess)

Calculate the error by individually the previous value from the new guess.|53 - 104| = 5151 > 0.001

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

3

Next, we must divide 208 by the an outcome of the previous action (53).208/53 = 3.9245

Calculate the arithmetic mean of this worth (3.9245) and also the result of action 2 (53).(53 + 3.9245)/2 = 28.4623 (new guess)

Calculate the error by individually the previous value from the brand-new guess.|28.4623 - 53| = 24.537724.5377 > 0.001

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

4

Next, we have to divide 208 by the an outcome of the previous step (28.4623).208/28.4623 = 7.3079

Calculate the arithmetic typical of this worth (7.3079) and the an outcome of step 3 (28.4623).(28.4623 + 7.3079)/2 = 17.8851 (new guess)

Calculate the error by individually the previous value from the brand-new guess.|17.8851 - 28.4623| = 10.577210.5772 > 0.001

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

5

Next, we should divide 208 through the result of the previous action (17.8851).208/17.8851 = 11.6298

Calculate the arithmetic typical of this value (11.6298) and the an outcome of step 4 (17.8851).(17.8851 + 11.6298)/2 = 14.7575 (new guess)

Calculate the error by individually the previous value from the brand-new guess.|14.7575 - 17.8851| = 3.12763.1276 > 0.001

Repeat this action again as the margin the error is better than than 0.001

6

Next, we must divide 208 through the an outcome of the previous action (14.7575).208/14.7575 = 14.0945

Calculate the arithmetic mean of this value (14.0945) and also the an outcome of step 5 (14.7575).(14.7575 + 14.0945)/2 = 14.426 (new guess)

Calculate the error by subtracting the previous value from the brand-new guess.|14.426 - 14.7575| = 0.33150.3315 > 0.001

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

7

Next, we must divide 208 by the an outcome of the previous step (14.426).208/14.426 = 14.4184

Calculate the arithmetic mean of this value (14.4184) and also the result of step 6 (14.426).(14.426 + 14.4184)/2 = 14.4222 (new guess)

Calculate the error by individually the previous value from the new guess.|14.4222 - 14.426| = 0.00380.0038 > 0.001

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

8

Next, we should divide 208 by the an outcome of the previous step (14.4222).208/14.4222 = 14.4222

Calculate the arithmetic mean of this worth (14.4222) and also the result of step 7 (14.4222).(14.4222 + 14.4222)/2 = 14.4222 (new guess)

Calculate the error by individually the previous worth from the new guess.|14.4222 - 14.4222| = 00

Result✅ We uncovered the result: 14.4222 In this case, that took us eight procedures to find the result.