Question

5.Arătați că următoarele numere sunt pătrate perfecte;
A.16×25; B.2la puterea18×3la puterea6;
C.25×3la puterea18; D.16×100; E.4la puterea15×121la puterea17; F.5la puterea14×7la puterea8×13la puterea24; G.3la puterea25+3la puterea34; H.2la puterea25-7×2la puterea20.

Answer 1

Explicație pas cu pas:

A.

16×25 = 4²×5² = (4×5)² = 20²

B.

2¹⁸×3⁶ = (2⁹)²×(3³)² = (2⁹×3³)²

C.

25×3¹⁸ = 5²×(3⁹)² = (5×3⁹)²

D.

16×100 = 4²×10² = (4×10)²

E.

4¹⁵×121¹⁷ = (2²)¹⁵×(11²)¹⁷ = (2¹⁵)²×(11¹⁷)² = (2¹⁵×11¹⁷)²

F.

5¹⁴×7⁸×13²⁴ = (5⁷)²×(7⁴)²×(13¹²)² = (5⁷×7⁴×13¹²)²

G.

3²⁵+3³⁴ = 3³⁴(3+1) = (3¹⁷)²×4 = (3¹⁷)²×2² = (2×3¹⁷)²

H.

2²⁵-7×2²⁰ = 2²⁰(2⁵-7) = (2¹⁰)²×25 = (2¹⁰)²×5² = (5×2¹⁰)²

q.e.d.