The SECRET Trick to Solving Nested Square Roots Revealed! #maths

The SECRET Trick to Solving Nested Square Roots Revealed! #maths

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[TankucT_AC]

Solution in Python:
from math import sqrt

def rec(n, cnt):
if cnt > 100: return sqrt(n)
return sqrt(n*rec(n, cnt+1))

print(rec(2, 0))
#output: ≈ 2

[Гантөгс.Б]

Solution by infinite descending geometric progression math:

finding root x

x=b1/1-q

b1-first number’s root(1/2)
q-is common ratio of the progression(in this case its 1/2)

Answer:

x=0.5/1-0.5 = 0.5/0.5 = 1
2’s 1 root

[logank]

The more rigorous method would be to write exponents rather than radicals to show that this is actually 2 raised to the power of a convergent infinite series. Essentially, 1/2 + 1/4 + … = 1.

[alifmoohammadalif-urrahman]

College teacher ❌❌❌❌❌❌❌♾️
YouTube guy ✅✅✅✅✅✅✅✅♾️

[thermitty_qxr]

It's because when you write it in exponential form, the exponent approaches 1

√(2√(2)) = 2^(3/4) or 0.75
√(2√(2√(2√2))) = 2^(15/16) or 0.9375
...
= 2^1

[mrmimi]

It's actually does make sense because it's just in reality

2^(1/2 + 1/4 + 1/8 + 1/16 + 1/32 ... ) which is just a series that end up to be equals to 1 so it's 2¹= 2

[dscocubes]

I used a different method but roughly same idea

[BHRocket]

This problem can also be solved using infinite gp method
√2√2√2... =2^1/2 × 2^1/4 × 2^1/8....
=2^[1/2 + 1/4 + (This is in the form of
= 2^1 Infinite gp so, sum.
=2 Infinite g.p =a/(1-r)
Where a=first term
r=common ratio
By using we can say 1/2÷(1-1/2)=1

=

[Why-kb_]

let √2√2√2...=x
√2x=x
x²=2x
x(x-2)=0
x=0 or x=2
as √y≥0, x=2
ans:√(2√(2√...))=2

[Boxed_Together]

basically if you do that to any number, you get the response to be that number

[UlkaPatil-ggot]

Here us a method factorise 2 and then the biggest factoriser is the ans.😊😊

[PhilosophicalNonsense-wygy]

Or it can be done as 2^(1/2+1/4+1/8...) where the exponent is 1 according to infinite series

[PEACEFUL_UMMAH_]

Me as a 10th student without watching the
let,

=>X²=2x(BCZ,
=>X²/X=2
=>X=2

[PeacefulCondorBird-guth]

😮😮😊😊 my methods and your method same 😅😅 but your calculations fast vissiolisatio

[NoNameforChannel_]

x² = 2x
x * x = 2x
x = 2x/x
x = 2
Easy

[Damnpower]

You can't do that bro because the that x isn't the same x when you replace it

[KhusbuGupta-oqkd]

The answer is 2. Let
x=√2+x
Or, X²=(√2+x)²
Or, x²-x-2=0
Or, (x-2)(x+1)=0
so, X=2answer, because under -ve sign number can't be answer

[dalitlegreenfuzzyman]

How do you know it’s greater than zero?

[RGS_]

Wait… so you know when he substitutes x into the top equation, how is that able to be substituted in? Is it because it’s infinite?

[SkillerAstro]

That doesn‘t make any sense

x^2 is not equal to 2x

Lets say x is 5
2x = 10
x^2 = 25
And 25 is not equal to 10