Newtons Method sqrt(7)

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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
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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?

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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