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:
What is the Answer?
How does the Babylonian Method Calculator work?
This calculator has 1 input.
What 3 formulas are used for the Babylonian Method Calculator?
If n is even, we set d = 2n + 2
If n is odd, we set d = 2n + 1
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
