Question

14. Arătaţi că următoarele numere naturale sunt cuburi perfecte (numărul natural a se numește cub perfect dacă există un număr natural b, astfel încât a = b): b) 451, f) 1742; Matema a) 369 e) 1933 c) 861 g) 2728; d) 521; h) 6423 55​

Answer 1

Răspuns:

$\bf a)~~3^{69} = 3^{23\cdot 3} =\red{\Big(3^{23}\Big)^{3}}\rightarrow cub ~perfect$

$\bf b)~~4^{51} =4^{17\cdot 3} =\blue{\Big(4^{17}\Big)^{3}}\rightarrow cub ~perfect$

$\bf c)~~8^{61} =\Big(2^{3}\Big)^{61} =2^{61\cdot 3} =\purple{\Big(2^{61}\Big)^{3}}\rightarrow cub ~perfect$

$\bf d)~~5^{21} = 5^{7\cdot 3} =\green{\Big(5^{7}\Big)^{3}}\rightarrow cub ~perfect$

$\bf e)~~19^{33} = 19^{11\cdot 3} =\purple{\Big(19^{11}\Big)^{3}}\rightarrow cub ~perfect$

$\bf f)~~17^{42} = 17^{14\cdot 3} =\red{\Big(17^{14}\Big)^{3}}\rightarrow cub ~perfect$

$\bf g)~~27^{28} =\Big(3^{3}\Big)^{28} =3^{28\cdot 3} =\pink{\Big(3^{28}\Big)^{3}}\rightarrow cub ~perfect$