Which Number is Greatest?

 Which Number is Greatest?

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Which is Greatest Number?

2⁹⁰⁰, 3⁶⁰⁰, 4⁴⁵⁰, 5³⁰⁰

Which is Smallest Number?

3√5, √6, 5√3

 

1)             2⁹⁰⁰, 3⁶⁰⁰, 4⁴⁵⁰, 5³⁰⁰

H.C.F of 900,600,450 & 300=150

900=2*450=2*3*150

600=2*300=2*2*150

450=2*225=2*3*75=3*150

300=2*150

2⁹⁰⁰=2^6*150= (2⁶)¹⁵⁰= (64)¹⁵⁰

3⁶⁰⁰=3^4*150= (3⁴)¹⁵⁰ = (81) ¹⁵⁰

4⁴⁵⁰=4^3*150= (4³)¹⁵⁰= (48) ¹⁵⁰

5³⁰⁰=5^2*150= (5²)¹⁵⁰ = (25) ¹⁵⁰

Greatest Number is 3⁶⁰⁰

 

2)         3√5, √6, 5√3

(5)^1/3, (6)^1/2, (3)^1/5

 

L.C.M of 3, 2, and 5 is 30

 

(5)^1/3= (5)^1*10/3*10= (5)^10/30= (9765625)^1/30

(6)^1/2= (6)^1*15/2*15= (6)^15/30= (470184984576)^1/30

(3)^1/5= (3)^1*6/5*6= (3)^6/30=(729)^1/30

Smallest Number is 5√3