Question

Arătați că următoarele numere sunt pătrate perfecte:​

Answer 1

Răspuns:

Explicație pas cu pas:

a = 7^2*11^2 = (7*11)^2 = 77^2 patrat perfect

b = 4^13*9 = (2^2)^13*3^2 = (2^13)^2 * 3^2 = (2^13*3)^2 patrat perfect

c = 4^9*9^2 = (2^2)^9 * 9^2 = (2^9*9)^2 patrat perfect

d = 2^6*3^6 = (2*3)^6 = 6^6 = (6^3)^2 patrat perfect

e = 5^24*7^6 = (5^12*7^3)^2 patrat perfect

f = 6^5*24^3 = 2^5*3^5*3^3*2^9 = 2^14*3^8 = (2^7*3^4)^2 patrat perfect

pt f: 6^5 = (2*3)^5 = 2^5*3^5

      24^3 = (2^3*3)^3 = 2^9*3^3