Binomial Approximation

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[田村博志-zy]

Set a:= 623^( 1/4 ). Then we have
2 = 625 - 623
= 5^4 - a^4
= ( 5^2 + a^2 )( 5 + a )( 5 - a )
By using 4 < a < 5, we have
( 5^2 + 4^2 )( 5 + 4 )( 5 - a ) < 2 < ( 5^2 + 5^2 )( 5 + 5 )( 5 - a )
Then we get approximated value of a as
5 - 2/369 < a < 5 - 1/250

According to sharper estimation, we may use
( 5^2 + 4^2 )( 5 + a )( 5 - a ) < 2 < ( 5^2 + 5^2 )( 5 + a )( 5 - a )

[kumkum]

You really cleared my doubt
You are 🙏🙏

[praveenjain]

Bro I feel very bad for u
U are very under rated
Bro u deserve a million subs

[theamanshortss]

starting cleared but last one is not clear

[SHRISTYKUMARI-wyrw]

1000^1/3 is equal to 10
How????
And
625^1/4 is equal to 5

[srijalupadhyay]

Rataa marke aaye ho kya bhai... bas direct amswer de rhe ho

[djsniper]

I don't understand how you cut and how you write 999/1000 in 3:55 😭

[vishnukesarwani]

How 999/1000 is coming I didn't understand