Question

descompuneti in factori primi numerele urmatoare si aratati ca sunt patrate perfecte : 1) 36 b)1 c)121 d) 9 e)289 f)3 la a 2 a x 16 g) 25 x 81 x 7 la a 2 a h) 4 la a 5 a x 5 la a 5 a i) 25 la a 3 a x (-7) la a 10 a j) 121 x 49 la a 3 a

Answer 1

Numerele descompuse in factori primi

1) 36 = 2x2x3x3

2) 1 = 1 (nu este numar prim)

3) 121 = 11x11

4) 9 = 3x3

5) 289 = 17x17

6) 3²x16 = 3x3x2x2x2x2

7) 25x81x7² = 5x5x3x3x3x3x7x7

8) 4⁵x5⁵ = 2x2x2x2x2x2x2x2x2x2x5x5x5x5x5

9)25³x(-7)¹⁰ = (5²)³x 7¹⁰ = 5x5x5x5x5x5x7x7x7x7x7x7x7x7x7x7

10) 121x49³ = 11x11x7x7x7x7x7x7

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Patrate perfecte:

1) 36 = 6² = patrat perfect

2) 1 = 1² = patrat perfect

3) 121 = 11²= patrat perfect

4) 9 = 3²= patrat perfect

5)  289 = 17²= patrat perfect

6) 3²·16 = 3²·4² = (3·4)² = 12²= patrat perfect

7) 25x81x7² = 5²×9²×7² = (5×9×7)² = 315²= patrat perfect

8)  4⁵x5⁵ = (2²)⁵x5⁵ = (2⁵)²x5⁴x5 = (32x25)²x5 = nu este patrat perfect

9) 25³x(-7)¹⁰ = (5²)³x 7¹⁰ = 5²ˣ³ x 7²ˣ⁵ = (5³)² x (7⁵)² = (5³x7⁵)² =

= patrat perfect

10) 121x49³ = 11²×7² = (11x7)² = 77² =  patrat perfect