Calcola l'espressione con i radicali

Problema:

Calcolare la seguente espressione:

$\sqrt{\sqrt{\frac{1}{16}+\sqrt{1+\frac{5}{4}}}-0,89}$

Soluzione:

$\sqrt{\sqrt{\frac{1}{16}+\sqrt{1+\frac{5}{4}}}-0,89}=\sqrt{\sqrt{\frac{1}{16}+\sqrt{\frac{9}{4}}}-\frac{89}{100}}=\sqrt{\sqrt{\frac{1}{16}+\frac{3}{2}}-\frac{89}{100}}=\sqrt{\sqrt{\frac{25}{16}}-\frac{89}{100}}=\sqrt{\frac{5}{4}-\frac{89}{100}}=\sqrt{\frac{36}{100}}=\frac{6}{10}=\frac{3}{5}$

cominciamo dalla radice più interna:

1)  radicequadrata(1 + 5/4) = radice[(4 +5)/4] = radice(9/4) = 3/2;

2)  radice quadrata(1/16 + 3/2)= radice[1/16 + 24/16) = radice(25/16) = 5/4;

0,89 = 89/100;

3)  radicequadrata[5/4 - 89/100] =

= radice quadrata[(125 - 89/100] = radice(36/100) =

= 6/10 =

= 3/5.

@alby ciao.

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$\small \sqrt{\sqrt{\dfrac{1}{16}+\sqrt{1+\dfrac{5}{4}}}-0,89}$

$\small \sqrt{\sqrt{\dfrac{1}{16}+\sqrt{\dfrac{4+5}{4}}}-\dfrac{89}{100}}$

$\small \sqrt{\sqrt{\dfrac{1}{16}+\sqrt{\dfrac{9}{4}}}-\dfrac{89}{100}}$

$\small \sqrt{\sqrt{\dfrac{1}{16}+\dfrac{3}{2}}-\dfrac{89}{100}}$

$\small \sqrt{\sqrt{\dfrac{1+24}{16}}-\dfrac{89}{100}}$

$\small \sqrt{\sqrt{\dfrac{25}{16}}-\dfrac{89}{100}}$

$\small \sqrt{\dfrac{5}{4}-\dfrac{89}{100}}$

$\small \sqrt{\dfrac{125-89}{100}}$

$\small \sqrt{\dfrac{\cancel{36}^9}{\cancel{100}_{25}}}$

$\small \sqrt{\dfrac{9}{25}}$

$\small \dfrac{3}{5}$