Question

Aratati ca urmatoarele numere sunt patrate perfecte: a)36 b)7^4 c)3^2×9 d)17^20 e)2^5×8^7 f)3^9×27^5​

Answer 1

Răspuns:

Explicație pas cu pas:

a)   36 = 6² → patrat perfect

b)   7⁴ = ( 7² )² = 49²  → patrat perfect

c)   3² x 9 = 9 x 9 = 9²  → patrat perfect

d)    17²⁰ = ( 17¹⁰ )² → patrat perfect

e)    2⁵ x 8⁷ = 2⁵ x 2⁽³ˣ⁷⁾ = 2⁽⁵⁺²¹⁾ = 2²⁶ = (2¹³)² → patrat perfect

sau:

=  ( 2⁵ x 8⁵ ) x 8² = ( 2 x 8)⁵ x 8² = 16⁵ x 8² =

= 4²ˣ⁵ x 8²=

= ( 4⁵ x 8)² → patrat perfect

f)  3⁹ x 27⁵ = 3⁹ x 3⁽³ˣ⁵⁾ = 3⁽⁹⁺¹⁵⁾ = 3²⁴ = (3¹²)²  → patrat perfect