Question

Step and justification of root√3.5​

Answer 1

$\large \boxed{ \boxed{ \sqrt{3.5} }}$

In this case, we are going to use the 'Babylonian method to get the square root of any positive number.We must define an error for the final result.Say, less than 0.01. In other words, we will try to find the value of the square root to at least 1 correct decimal places.

Step 1:

• Divide the number (3.5) by 2 to get the first guess for the square root. first guess = 3.5 / 2 = 1.75.

Step 2:

• Divide 3.5 by the result obtained in step
• previous. d = 3.5 / 1.75 = 2.
• Roll the arithmetic mean of (d) and the obtained value
• in step 1: (2 +1.75) / 2 = 1.875 (new

approach).

• Error = new guess - previous value = 1.75 1.875 = 0.125.
• 0.125 0.01. As the error> accuracy, please repeat this
• t happened one more time.

Step 3:

• Divide 3.5 by the result obtained in the previous step. d = 3.5 / 1.875 = 1.8666666667.
• Roll the arithmetic mean of (d) and the value obtained in step 2: (1.8666666667 + 1.875) / 2 =1.8708333334 (new approximation).
• Error = new guess - previous value = 1.875 -1.8708333334 = 0.0041666666

• 0.0041666666 <0.01. Once the error <accuracy, stop the process and use 1.8708333334 as the final value for the square root.
• Then we can say that the square root of 3.5 is 1.87 with an error less than 0.01 (actually the error is 0.0041666666). This means that the first 2 decimal places are correct. Just for comparison, the returned value using the javascript function Math.sqrt (3.5) 'is 1.8708286933869707.

Note: There are other ways to calculate square root. This is just one of them.

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