As friend should know from her high college algebra course, the square source y that a number x is such that y2 = x. By multiply the value y through itself, we acquire the worth x. For instance, 16.9706 the square root of 288 because 16.97062 = 16.9706×16.9706 = 288.

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Square root of 288 = 16.9706

## Is 288 a Perfect Square Root?

No. The square root of 288 is no an integer, hence √288 isn"t a perfect square.

Previous perfect square root is: 256

Next perfect square source is: 289

## How perform You leveling the Square root of 288 in Radical Form?

The main suggest of simplification (to the simplest radical type of 288) is as follows: obtaining the number 288 inside the radical authorize √ as low together possible.

288= 2 × 2 × 2 × 2 × 2 × 3 × 3= 122

## Is the Square root of 288 rational or Irrational?

Since 288 isn"t a perfect square (it"s square source will have an infinite number of decimals), it is an irrational number.

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

StepSequencing
1

In action 1, we must make our very first guess around the value of the square root of 288. To execute this, division the number 288 through 2.

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As a result of separating 288/2, we gain the an initial guess: 144

2

Next, we must divide 288 by the result of the previous step (144).288/144 = 2

Calculate the arithmetic mean of this value (2) and the an outcome of step 1 (144).(144 + 2)/2 = 73 (new guess)

Calculate the error by individually the previous value from the new guess.|73 - 144| = 7171 > 0.001

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

3

Next, we must divide 288 through the result of the previous action (73).288/73 = 3.9452

Calculate the arithmetic average of this value (3.9452) and also the result of action 2 (73).(73 + 3.9452)/2 = 38.4726 (new guess)

Calculate the error by subtracting the previous worth from the brand-new guess.|38.4726 - 73| = 34.527434.5274 > 0.001

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

4

Next, we have to divide 288 through the result of the previous step (38.4726).288/38.4726 = 7.4858

Calculate the arithmetic typical of this value (7.4858) and the an outcome of step 3 (38.4726).(38.4726 + 7.4858)/2 = 22.9792 (new guess)

Calculate the error by subtracting the previous value from the brand-new guess.|22.9792 - 38.4726| = 15.493415.4934 > 0.001

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

5

Next, we have to divide 288 by the result of the previous action (22.9792).288/22.9792 = 12.5331

Calculate the arithmetic typical of this value (12.5331) and also the result of step 4 (22.9792).(22.9792 + 12.5331)/2 = 17.7562 (new guess)

Calculate the error by individually the previous value from the new guess.|17.7562 - 22.9792| = 5.2235.223 > 0.001

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

6

Next, we should divide 288 through the result of the previous action (17.7562).288/17.7562 = 16.2197

Calculate the arithmetic median of this value (16.2197) and the result of action 5 (17.7562).(17.7562 + 16.2197)/2 = 16.988 (new guess)

Calculate the error by subtracting the previous value from the new guess.|16.988 - 17.7562| = 0.76820.7682 > 0.001

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

7

Next, we need to divide 288 through the an outcome of the previous step (16.988).288/16.988 = 16.9531

Calculate the arithmetic typical of this worth (16.9531) and also the result of step 6 (16.988).(16.988 + 16.9531)/2 = 16.9706 (new guess)

Calculate the error by subtracting the previous value from the new guess.|16.9706 - 16.988| = 0.01740.0174 > 0.001

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

8

Next, we have to divide 288 by the result of the previous step (16.9706).288/16.9706 = 16.9705

Calculate the arithmetic typical of this value (16.9705) and the an outcome of step 7 (16.9706).(16.9706 + 16.9705)/2 = 16.9706 (new guess)

Calculate the error by individually the previous value from the new guess.|16.9706 - 16.9706| = 00

Result✅ We found the result: 16.9706 In this case, that took united state eight steps to uncover the result.