Question

aratati ca urmatoarele numere sunt patrate perfecte : a) 4^15×121^17 b) 5^14×7^8×13^24 c) 3^25+3^34 d)2^25-7×2^20​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 4^15×121^17 = (2^2)^15 * (11^2)^17 = (2^15)^2 * (11^17)^2 = (2^15*11^17)^2 patrat perfect

b) 5^14×7^8×13^24 = (5^7)^2*(7^4)^2*(13^12)^2 = (5^7*7^4*13^12)^2 patrat perfect

c) 3^25+3^34 = 3^34*(3 + 1) = 4*3^34 = (2^2)^2*(3^17)^2 = (2^2*3^17)^2 patrat perfect

d )2^25-7×2^20​ = 2^20(2^5 - 7) = 2^20(32 - 7) = 25*2^20 = 5^2*(2^10)^2 =

= (5*2^10)^2 patrat perfect