approximate 4th root of 75, Newton's Method, calculus 1 tutorial

We will use Newton's method to approximate the irrational number, the fourth root of 75.
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#justcalculus

[exynosnemea]

After a long day of doing calculus, it's fun to go back to approximating irrationals in a new way. Thanks Steve. Stay being a Gigachad.

[volodymyrgandzhuk]

Fun fact: if you try to approximate √75 with the tangent/differential method Steve showed in one of his videos, and then do the same thing for the square root of the result (because the 4th root is basically the square root of the square root), you will get exactly what he got here the first time he applied the Newton method formula.

[kabirsethi]

I have another method. The closest perfect power is 81 which is 3^4. Now we know that 81>75 so 3>fourth root(75). Now that means obviously, 3-fourth root(75)>0 . now raise this to the power 4. This becomes, 156-108 cube root(75)+270 root3-60 fourth root (675)>0 now upon some rearrangement we get that, cuberoot75>156+270 root3- fourth root(675) all divided by 108. This is tedious but it gives the very close approximation of fourth root of 75. Please correct me if there are errors

[jacobcarlson]

I was working on the derivative on natural log in calculus and attempted to find the derivative of and I would like to see your approach.
(sorry if it is hard to read based on how I typed it.

[manthing]

3:45 reading aloud, reminded me about that olympiad problem you also did (you were also saying number 4 a lot in that video). Calculate the sum of digits of the sum of the digits of the sum of the digits of the number 4444⁴⁴⁴⁴(i think).

[mikejackson]

Thanks for this, Steve! I have learnt something new! 😀😀😀

[Mathematician]

Learned something great bro. May you live healthy, wealthy brainy and long.

[etgaming]

I got lost halfway through but then it all made sense by the end👌🏻 this is a cool method that I have never heard of before and I have a physics degree.

[its_lucky]

fourth root of 75 is same as 75^1/4. this means to mupltiple 75 by 1/4 of itself, so 17.5/4 = 18.75

[jackomeme]

Isn't the algorithm used in the fast inverse square root of quake 3 ?

[joewilson]

Very clear method thank you, helped a lot!!

[idkyet]

just when i thought this would be good for olympiad...

also i just realised olympiad questions would probably have all the √s cancel out or be a perfect square

[wryanihad]

Is this formula used also in calculator

[SampleroftheMultiverse]

13
This process’s load deflection curve is sawtooth like in your video

Mechanical properties related to a unique variation of Euler’s Contain Column studies.

It shows how materials (representing fields) naturally respond to induced stresses in a “quantized“ manor.

This process, unlike harmonic oscillators can lead to formation of stable structures.

The quantized responses closely models the behaviors known as the Quantum Wave Function as described in modern physics.

The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems.

The model shows the known requirement of exponential load increase and the here-to-for unknown collapse of resistance during transition, leading to the very fast jump to the next energy levels.

This is shown by the saw-tooth graph’s bifurcation during the quantum jump.

In materials the process continues till the load passes the ultimate tensile strength. Fields are not bounded by these conditions.

[Rafi_Bin_Haider-Ali]

My man put microphone into pokemon ball💀💀

[madhavsoni]

using differentials with linear approximation is far just an oπnion

[neutronenstern.]

well if i want to approx it in my head i will still stick to try and error i guess.

[Ayyouboss]

Imagine using a calculator to use newtons method but not being able to calculate sqrt(75) 😄

[DilipKumar-nskl]

We may use a general formula to find the nth root of x given that x^n.=N.
General formula

x=[(n-1)x+{N/x^(n-1)}]/n
m+1 m m
Here n=4, N=75.
Taking m =1 & x=3 we get
1
x=[(4-1)3+{75/3^3}]/4
2
x=2.9428322282
3
x=2.942830956
4
x=2.942830956
5
Hence x=2.942830956.

[holyshit]

I would calculate square root twice with paper and pencil method
In paper and pencil method I need to calculate twice as much digits for the first square root as I want in final result
With paper and pencil method i calculated up to 4 digits after decimal point