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Today topic : A Nice square root math simplification
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[@himo3485]

2^100*(2^2)^100*(2^3)^100=2^100*2^200*2^300=2^600=(2^100)^6=x^6 x=2^100

[@MathEducation100M]

Nice trick

[@andryvokubadra2644]

2^100*4^100*8^100 = x^6
(2¹*2²*2³)^100 = x^6
(±2³*²)^100 = x^6
(±2^100)^6 = x^6
±2^100 = x 2:29

[@hangthuy458]

2^100×2^2×100×2^3×100=2^100+200+300
=2^600=x^6
=2^100×6=x^6
X=2^100

[@Sprutolog]

This could be correct in case the task was to find natural solutions. At least, -2^100 is an obvious real answer, plus complex solutions

[@adgf1x]

2^600=x^6=>(2^100)^6=x^6=>x=2^100.ans

[@吳昶霖]

8^100×8^100
=2^（3×200）=2^600
2^600=x^6. X=2^100

[@oahuhawaii2141]

x = ± 2¹⁰⁰ , 2⁹⁹ * (1 ± i*√3) , 2⁹⁹ * (-1 ± i*√3)

[@吳昶霖]

X=2^100

[@ayanchik03]

It actually has another 5 solutions

[@oahuhawaii2141]

x = ± 2¹⁰⁰ , 2⁹⁹ * (1 ± i*√3) , 2⁹⁹ * (-1 ± i*√3)

[@JamesGaunt369]

What about -2^100 ?

[@andryvokubadra2644]

-2^100 too. . .
x = ±2^100

[@oahuhawaii2141]

x = ± 2¹⁰⁰ , 2⁹⁹ * (1 ± i*√3) , 2⁹⁹ * (-1 ± i*√3)

[@paysongeorge7080]

A google

[@oahuhawaii2141]

Not quite a googol (10¹⁰⁰):
10¹⁰⁰ = 2¹⁰⁰ * 5¹⁰⁰
It's off by more than the square of 2¹⁰⁰ .
The cube root of a googol is closer.

[@rleroygordon]

2^100 = 2^(4 * 25) =
(2^25)^4 =
(33,554,432)^4 =
(33,554,432)^(2 * 2) =
[(33,554,432)^2]^2 =
(1,125,899,906,842,624)^2
I'll let someone with a calculator that has more places take it from here.

[@oahuhawaii2141]

x = ± 2¹⁰⁰ , 2⁹⁹ * (1 ± i*√3) , 2⁹⁹ * (-1 ± i*√3)

[@АндрейАнцышкин]

😮2 в 100 это Сколько ❓

[@ChavoMysterio]

x⁶=2¹⁰⁰•4¹⁰⁰•8¹⁰⁰
x⁶=2¹⁰⁰•(2¹⁰⁰)²•(2¹⁰⁰)³
x⁶=(2¹⁰⁰)⁶
x=±2¹⁰⁰ ❤❤
4 non real roots

[@oahuhawaii2141]

x = ± 2¹⁰⁰ , 2⁹⁹ * (1 ± i*√3) , 2⁹⁹ * (-1 ± i*√3)

[@oahuhawaii2141]

2¹⁰⁰ * 4¹⁰⁰ * 8¹⁰⁰ = x⁶
2¹⁰⁰ * (2²)¹⁰⁰ * (2³)¹⁰⁰ = x⁶
2¹⁰⁰ * 2²⁰⁰ * 2³⁰⁰ = x⁶
2¹⁰⁰⁺²⁰⁰⁺³⁰⁰ = x⁶
2⁶⁰⁰ = x⁶
x = 2¹⁰⁰ * cis(k*60⁰) , k ∈ { 0, ±1, ±2, 3 }
x = ± 2¹⁰⁰ , 2⁹⁹ * (1 ± i*√3) , 2⁹⁹ * (-1 ± i*√3)