Spiegare gentilmente i ragionamenti e argomentare.
Problema:
Calcolare la seguente espressione:
$\sqrt{\frac{13}{16}+\sqrt{0,25}+\sqrt{0,0625}}$
Soluzione:
$\sqrt{\frac{13}{16}+\sqrt{0,25}+\sqrt{0,0625}}=\sqrt{\frac{13}{16}+\sqrt{\frac{25}{100}}+\sqrt{\frac{625}{10000}}}=\sqrt{\frac{13}{16}+\frac{5}{10}+\frac{25}{100}}=\sqrt{\frac{13}{16}+\frac{1}{2}+\frac{1}{4}}=\sqrt{\frac{25}{16}}=\frac{5}{4}$.
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$\small \sqrt{\dfrac{13}{16}+\sqrt{0,25}+\sqrt{0,0625}}$
$\small \sqrt{\dfrac{13}{16}+\sqrt{\dfrac{\cancel{25}^1}{\cancel{100}_4}}+\sqrt{\dfrac{\cancel{625}^1}{\cancel{10000}_{16}}}}$
$\small \sqrt{\dfrac{13}{16}+\sqrt{\dfrac{1}{4}}+\sqrt{\dfrac{1}{16}}}$
$\small \sqrt{\dfrac{13}{16}+\dfrac{1}{2}+\dfrac{1}{4}}$
$\small \sqrt{\dfrac{13+8+4}{16}}$
$\small \sqrt{\dfrac{25}{16}}$
$\small \dfrac{5}{4}$