Question

Aratati ca urmatoarele numere sunt patrate perfecte

A)9,36,64,121,400

B)3 la puterea 2 ×16, 25×81×7la puterea2, 4la puterea5 ×4 la puterea 4, 25 la puterea 3-7 la puterea 10, 121×49 la puterea 3

Answer 1

Explicație pas cu pas:

a)

9 = 3 • 3 = 3^2

36 = 6 • 6 = 6^2

64 = 8 • 8 = 8^2

121 = 11 • 11 = 11^2

400 = 20 • 20 = 20^2

b)

3^2 • 16 = 3^2 • 4^2 = (3•4)^2 = 12^2

25 • 81 • 7^2 = 5^2 • 9^2 • 7^2 = (5•9•7)^2 = 315^2

4^5 • 4^4 = (2^2)^5 • (2^2)^2 = (2^5)^2 • 4^2 = 32^2 • 4^2 = (32•4)^2 = 128^2

25^3 -7^10 = (5^2)^3 • (7^5)^2 = (5^3)^2 • (7^5)^2 = (5^3 • 7^5)^2

121 • 49^3 = 11^2 • (7^2)^3 = 11^2 • (7^3)^2 = (11 • 7^3)^2

^ = simbol folosit pentru ridicarea la putere

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formule generale:

a^n • b^n = (a•b)^n

(a^n)^m = (a^m)^n

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