As you must understand 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 acquire 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 not an integer, therefore √208 isn"t a perfect square.

Previous perfect square root is: 196

Next perfect square root is: 225


How Do You Simplify the Square Root of 208 in Radical Form?

The main allude of simplification (to the most basic radical form of 208) is as follows: gaining the number 208 inside the radical sign √ as low as possible.

208= 2 × 2 × 2 × 2 × 13= 413

Therefore, the answer is 413.


Is the Square Root of 208 Rational or Irrational?

Because 208 isn"t a perfect square (it"s square root will certainly have actually an boundless number of decimals), it is an irrational number.


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

StepSequencing
1

In step 1, we need to make our first guess about the value of the square root of 208. To execute this, divide the number 208 by 2.

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As a result of separating 208/2, we obtain the initially guess: 104

2

Next off, we must divide 208 by the outcome of the previous action (104).208/104 = 2

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

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

Repeat this action aget as the margin of error is greater than than 0.001

3

Next off, we need to divide 208 by the result of the previous step (53).208/53 = 3.9245

Calculate the arithmetic intend of this worth (3.9245) and the outcome of step 2 (53).(53 + 3.9245)/2 = 28.4623 (brand-new guess)

Calculate the error by subtracting the previous worth from the new guess.|28.4623 - 53| = 24.537724.5377 > 0.001

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

4

Next, we must divide 208 by the outcome of the previous action (28.4623).208/28.4623 = 7.3079

Calculate the arithmetic mean of this worth (7.3079) and the result of step 3 (28.4623).(28.4623 + 7.3079)/2 = 17.8851 (brand-new guess)

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

Repeat this step aacquire as the margin of error is better than than 0.001

5

Next, we have to divide 208 by the outcome of the previous action (17.8851).208/17.8851 = 11.6298

Calculate the arithmetic suppose of this worth (11.6298) and the result of step 4 (17.8851).(17.8851 + 11.6298)/2 = 14.7575 (brand-new guess)

Calculate the error by subtracting the previous worth from the new guess.|14.7575 - 17.8851| = 3.12763.1276 > 0.001

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

6

Next off, we must divide 208 by the outcome of the previous step (14.7575).208/14.7575 = 14.0945

Calculate the arithmetic intend of this worth (14.0945) and also the outcome of step 5 (14.7575).(14.7575 + 14.0945)/2 = 14.426 (brand-new guess)

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

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

7

Next, we should divide 208 by the result of the previous action (14.426).208/14.426 = 14.4184

Calculate the arithmetic intend of this worth (14.4184) and the outcome of action 6 (14.426).(14.426 + 14.4184)/2 = 14.4222 (new guess)

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

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

8

Next off, we have to divide 208 by the outcome of the previous step (14.4222).208/14.4222 = 14.4222

Calculate the arithmetic intend of this worth (14.4222) and also the outcome of step 7 (14.4222).(14.4222 + 14.4222)/2 = 14.4222 (brand-new guess)

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

Result✅ We uncovered the result: 14.4222 In this situation, it took us eight steps to discover the result.