Enter Number


  

Given S = 50:

Calculate:√50 using the Newtons Method

Build Newtons Method

The square root of a number can be represented
ƒ(x) = x2 - S

Take the Derivative of this

ƒ'(x) = 2x

Since the square root > 0, start with x0 = 1

Calculate x1

x1 = x0 + (ƒ(x0) - S)/ƒ'(x0)

x1 = 1 + (12 - 50)/2(1)

x1 = 1 + (1 - 50)/2

x1 =1 + -49/2

x1 = 1 + -24.5

x1 = 25.5

Calculate x2

x2 = x1 + (ƒ(x1) - S)/ƒ'(x1)

x2 = 25.5 + (25.52 - 50)/2(25.5)

x2 = 25.5 + (650.25 - 50)/51

x2 =25.5 + 600.25/51

x2 = 25.5 + 11.769607843137

x2 = 13.730392156863

Calculate x3

x3 = x2 + (ƒ(x2) - S)/ƒ'(x2)

x3 = 13.730392156863 + (13.7303921568632 - 50)/2(13.730392156863)

x3 = 13.730392156863 + (188.52366878124 - 50)/27.460784313725

x3 =13.730392156863 + 138.52366878124/27.460784313725

x3 = 13.730392156863 + 5.0444177849648

x3 = 8.685974371898

Calculate x4

x4 = x3 + (ƒ(x3) - S)/ƒ'(x3)

x4 = 8.685974371898 + (8.6859743718982 - 50)/2(8.685974371898)

x4 = 8.685974371898 + (75.446150789269 - 50)/17.371948743796

x4 =8.685974371898 + 25.446150789269/17.371948743796

x4 = 8.685974371898 + 1.4647838975668

x4 = 7.2211904743312

Calculate x5

x5 = x4 + (ƒ(x4) - S)/ƒ'(x4)

x5 = 7.2211904743312 + (7.22119047433122 - 50)/2(7.2211904743312)

x5 = 7.2211904743312 + (52.145591866571 - 50)/14.442380948662

x5 =7.2211904743312 + 2.1455918665711/14.442380948662

x5 = 7.2211904743312 + 0.14856219858747

x5 = 7.0726282757437

Calculate x6

x6 = x5 + (ƒ(x5) - S)/ƒ'(x5)

x6 = 7.0726282757437 + (7.07262827574372 - 50)/2(7.0726282757437)

x6 = 7.0726282757437 + (50.022070726849 - 50)/14.145256551487

x6 =7.0726282757437 + 0.022070726849137/14.145256551487

x6 = 7.0726282757437 + 0.0015602917323416

x6 = 7.0710679840113

Final Answer

x6 = 7.0710679840113


You have 2 free calculationss remaining



What is the Answer?
x6 = 7.0710679840113
How does the Newton Method Calculator work?
Free Newton Method Calculator - Calculates the square root of a positive integer using the Newton Method
This calculator has 1 input.

What 3 formulas are used for the Newton Method Calculator?

ƒ(x) = x2 - S
ƒ'(x) = 2x
xn = xn - 1 + (ƒ(xn - 1) - S)/ƒ'(xn - 1)

For more math formulas, check out our Formula Dossier

What 3 concepts are covered in the Newton Method Calculator?

algorithm
A process to solve a problem in a set amount of time
newtons method
another numerical method for solving an equation f...
square root
a factor of a number that, when multiplied by itself, gives the original number
√x
Example calculations for the Newton Method Calculator
  1. Newton method sqrt(50)

Tags:



Add This Calculator To Your Website




An Automated Online Math Tutor serving 8.1 million parents and students in 235 countries and territories.

Our Services

Top Categories

Community