Enter Number
Given S = 7:
Calculate:√7 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 - 7)/2(1)
x1 = 1 + (1 - 7)/2
x1 =1 + -6/2
x1 = 1 + -3
x1 = 4
Calculate x2
x2 = x1 + (ƒ(x1) - S)/ƒ'(x1)
x2 = 4 + (42 - 7)/2(4)
x2 = 4 + (16 - 7)/8
x2 =4 + 9/8
x2 = 4 + 1.125
x2 = 2.875
Calculate x3
x3 = x2 + (ƒ(x2) - S)/ƒ'(x2)
x3 = 2.875 + (2.8752 - 7)/2(2.875)
x3 = 2.875 + (8.265625 - 7)/5.75
x3 =2.875 + 1.265625/5.75
x3 = 2.875 + 0.22010869565217
x3 = 2.6548913043478
Calculate x4
x4 = x3 + (ƒ(x3) - S)/ƒ'(x3)
x4 = 2.6548913043478 + (2.65489130434782 - 7)/2(2.6548913043478)
x4 = 2.6548913043478 + (7.0484478379017 - 7)/5.3097826086957
x4 =2.6548913043478 + 0.048447837901702/5.3097826086957
x4 = 2.6548913043478 + 0.0091242601575365
x4 = 2.6457670441903
Final Answer
x4 = 2.6457670441903
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What is the Answer?
x4 = 2.6457670441903
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 - Sƒ'(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?
algorithmA process to solve a problem in a set amount of timenewtons methodanother numerical method for solving an equation f...square roota factor of a number that, when multiplied by itself, gives the original number√x
Example calculations for the Newton Method Calculator
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