Babylonian Method sqrt(50)
Enter number for the Babylonian Method
Calculate √50 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:
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(50 + 50/50)
x1 = ½(50 + 1)
x1 = ½(51)
x1 = 25.5
Calculate x2
x2 = ½(x2 + S/x2)
x2 = ½(25.5 + 50/25.5)
x2 = ½(25.5 + 1.9607843137255)
x2 = ½(27.460784313725)
x2 = 13.730392156863
Calculate x3
x3 = ½(x3 + S/x3)
x3 = ½(13.730392156863 + 50/13.730392156863)
x3 = ½(13.730392156863 + 3.6415565869332)
x3 = ½(17.371948743796)
x3 = 8.685974371898
Calculate x4
x4 = ½(x4 + S/x4)
x4 = ½(8.685974371898 + 50/8.685974371898)
x4 = ½(8.685974371898 + 5.7564065767643)
x4 = ½(14.442380948662)
x4 = 7.2211904743312
Calculate x5
x5 = ½(x5 + S/x5)
x5 = ½(7.2211904743312 + 50/7.2211904743312)
x5 = ½(7.2211904743312 + 6.9240660771562)
x5 = ½(14.145256551487)
x5 = 7.0726282757437
Calculate x6
x6 = ½(x6 + S/x6)
x6 = ½(7.0726282757437 + 50/7.0726282757437)
x6 = ½(7.0726282757437 + 7.069507692279)
x6 = ½(14.142135968023)
x6 = 7.0710679840113
Build final answer:
√50 = 7.0710679840113
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What is the Answer?
√50 = 7.0710679840113
How does the Babylonian Method Calculator work?
Free Babylonian Method Calculator - 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?
D = Number of Digits to the left of the decimal pointIf n is even, we set d = 2n + 2
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?
algorithmA process to solve a problem in a set amount of timebabylonian methodA method to find square roots using dividing and averagingsquare roota factor of a number that, when multiplied by itself, gives the original number√x
Example calculations for the Babylonian Method Calculator
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