Babylonian Method sqrt(50)

Publish date: 2024-06-16
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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

You have 1 free calculations remaining


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 point
If 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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