Question

Aratati ca urmatoarele numere sunt patrate ale unor numere naturale: a)5^46,b)23^100,c)(7^6)^5,d)25^37,e)4 75,f)625^7,g)16x25,h)2^18x3^6,i)25x3^18.Pls repede 30 puncte

Answer 1

a) 5^46 = (5^23)^2
b) 23^100 = (23^50)^2
c) (7^6)^5 =- 7^30 = (7^15)^2
d) 25^37 = (5^2)^37 = 5^74 = (5^37)^2
e) 4^75 = (2^2)^75 = 2^150 = (2^75)^2
f) 625^7 = (5^4)^7 = 5^28 = (5^14)^2
g) 16 x 25 = (4^2) x (5^2) = 20^2
h) 2^18 x 3^6 = (2^9)^2 x (3^3)^2 = (2^9 x 3^3)^2
i) 25 x 3^18 = 5^2 x (3^9)^2 = (5 x 3^9)^2