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Babylonian Method sqrt(60)

Enter number for the Babylonian Method


  
Calculate √60 using Babylonian Method

Calculate D:

D = Number of Digits left of the decimal point
D = 2

Calculate n:

If n is even, d = 2n + 2.
If n is odd, d = 2n + 1.
Since d = 2 is even, d = 2n + 2
2 = 2(n) + 2

Subtract 2 from each side of the equation:

2 - 2 = 2(n) + 2 - 2
2n = 2 - 2
2n = 0

Divide each side of the equation by 2:

2n
2
=
  
0
2

n = 0

Calculate initial value x0:

If d is even, startup value = 6 x 10n.
If d is even, our initial startup value is 6 x 10n

Since 2 is even, startup value = 6 x 10n
6 x 100 = 6 x 1 = 6

Calculate x1
x1 = ½(x1 + S/x1)
x1 = ½(60 + 60/60)
x1 = ½(60 + 1)
x1 = ½(61)
x1 = 30.5

Calculate x2
x2 = ½(x2 + S/x2)
x2 = ½(30.5 + 60/30.5)
x2 = ½(30.5 + 1.9672131147541)
x2 = ½(32.467213114754)
x2 = 16.233606557377

Calculate x3
x3 = ½(x3 + S/x3)
x3 = ½(16.233606557377 + 60/16.233606557377)
x3 = ½(16.233606557377 + 3.6960363544559)
x3 = ½(19.929642911833)
x3 = 9.9648214559165

Calculate x4
x4 = ½(x4 + S/x4)
x4 = ½(9.9648214559165 + 60/9.9648214559165)
x4 = ½(9.9648214559165 + 6.0211816403771)
x4 = ½(15.986003096294)
x4 = 7.9930015481468

Calculate x5
x5 = ½(x5 + S/x5)
x5 = ½(7.9930015481468 + 60/7.9930015481468)
x5 = ½(7.9930015481468 + 7.5065667932857)
x5 = ½(15.499568341433)
x5 = 7.7497841707163

Calculate x6
x6 = ½(x6 + S/x6)
x6 = ½(7.7497841707163 + 60/7.7497841707163)
x6 = ½(7.7497841707163 + 7.742151094571)
x6 = ½(15.491935265287)
x6 = 7.7459676326436

Build final answer:

√60 = 7.7459676326436




What is the Answer?

√60 = 7.7459676326436

How does the Babylonian Method Calculator work?

Determines the square root of a number using the Babylonian Method.
This calculator has 1 input.

What 3 formulas are used for the Babylonian Method Calculator?

  1. D = Number of Digits to the left of the decimal point
  2. If n is even, we set d = 2n + 2
  3. If n is odd, we set d = 2n + 1

For more math formulas, check out our Formula Dossier

What 3 concepts are covered in the Babylonian Method Calculator?

algorithm
A process to solve a problem in a set amount of time
babylonian method
A method to find square roots using dividing and averaging
square root
a factor of a number that, when multiplied by itself, gives the original number
√x

Example calculations for the Babylonian Method Calculator

  1. Babylonian Method for 60

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