[Risolto] Aiuto Esercizio Matematica

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Trasforma in frazioni i seguenti numeri con decimali:

$1,\overline3 = \frac{13-1}{9} = \frac{12}{9} = \frac{4}{3}$;

$0,4 = \frac{4}{10} = \frac{2}{5}$;

$0,025 = \frac{25}{1000} = \frac{1}{40}$;

quindi, sostituendoli, reimpostiamo l'espressione:

$\sqrt{\big[(2,4+5,6)-\big(\frac{4}{3}-\frac{3}{8}+\frac{2}{5}-\frac{1}{40}\big)\big]·\frac{3^3}{2^2}}$ =

= $\sqrt{\big[8-\big(\frac{160-45+48-3}{120}\big)\big]·\frac{27}{4}}$ =

= $\sqrt{\big[8-\frac{160}{120}\big]·\frac{27}{4}}$ =

= $\sqrt{\big[8-\frac{4}{3}\big]·\frac{27}{4}}$ =

= $\sqrt{\big[\frac{24-4}{3}\big]·\frac{27}{4}}$ =

= $\sqrt{\frac{20}{3}·\frac{27}{4}}$ =

= $\sqrt{\frac{5}{1}·\frac{9}{1}}$ =

= $\sqrt{45}$ =

= $3\sqrt5$ $(≅ 6,7082$.