Question

radical 4375 _( radical 3087 plus radical 4732 _ radical 2268)

Answer 1

Pentru a putea scoate de sub radical trebuie sa descompunem in produs de factori primi

4375 | 5

875 | 5

 175 | 5

  35 | 5

    7 | 7

    1

4375=5⁴×7

$\sqrt{4375}=25\sqrt{7}$

3087 | 3

1029 | 3

 343 | 7

   49 | 7

     7 | 7

     1

3087=3²×7³

$\sqrt{3087} =21\sqrt{7}$

4732 | 2

2366 | 2

1183 | 7

 169 | 13

    13 | 13

      1

4732=2²×7×13²

$\sqrt{4732}=26\sqrt{7}$

2268 | 2

1134  | 2

  567 | 7

     81 | 3

     27 | 3

       9 | 3

       3 | 3

        1

2268=2²×3⁴×7

$\sqrt{2268} =18\sqrt{7}$

$\sqrt{4375} -(\sqrt{3087} +\sqrt{4732} -\sqrt{2268} )=\\25\sqrt{7} -(21\sqrt{7} +26\sqrt{7} -18\sqrt{7} )=$

Avand acelasi radical putem calcula coeficientii acestora:

$25\sqrt{7} -(47\sqrt{7} -18\sqrt{7} )=\\\\25\sqrt{7} -25\sqrt{7} =-4\sqrt{7}$

Un alt exercitiu gasesti aici: https://brainly.ro/tema/4746452

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