## 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:

n = 0

##### Calculate initial value x0:

If d is even, startup value = 6 x 10^{n}.

If d is even, our initial startup value is 6 x 10^{n}

Since 2 is even, startup value = 6 x 10^{n}

6 x 10^{0} = 6 x 1 = 6

##### Calculate x_{1}

x_{1} = ½(x_{1} + S/x_{1})

x_{1} = ½(60 + 60/60)

x_{1} = ½(60 + 1)

x_{1} = ½(61)

x_{1} = 30.5

##### Calculate x_{2}

x_{2} = ½(x_{2} + S/x_{2})

x_{2} = ½(30.5 + 60/30.5)

x_{2} = ½(30.5 + 1.9672131147541)

x_{2} = ½(32.467213114754)

x_{2} = 16.233606557377

##### Calculate x_{3}

x_{3} = ½(x_{3} + S/x_{3})

x_{3} = ½(16.233606557377 + 60/16.233606557377)

x_{3} = ½(16.233606557377 + 3.6960363544559)

x_{3} = ½(19.929642911833)

x_{3} = 9.9648214559165

##### Calculate x_{4}

x_{4} = ½(x_{4} + S/x_{4})

x_{4} = ½(9.9648214559165 + 60/9.9648214559165)

x_{4} = ½(9.9648214559165 + 6.0211816403771)

x_{4} = ½(15.986003096294)

x_{4} = 7.9930015481468

##### Calculate x_{5}

x_{5} = ½(x_{5} + S/x_{5})

x_{5} = ½(7.9930015481468 + 60/7.9930015481468)

x_{5} = ½(7.9930015481468 + 7.5065667932857)

x_{5} = ½(15.499568341433)

x_{5} = 7.7497841707163

##### Calculate x_{6}

x_{6} = ½(x_{6} + S/x_{6})

x_{6} = ½(7.7497841707163 + 60/7.7497841707163)

x_{6} = ½(7.7497841707163 + 7.742151094571)

x_{6} = ½(15.491935265287)

x_{6} = 7.7459676326436

##### Build final answer:

√60 = **7.7459676326436**

##### 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?

- 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

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