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radice quadrata[(10^2/28) : (15/7) : 25 : (5/3)] =

= radice quadrata[(100/28) x (7/15) : 25 : (5/3)] = 

(100/28 si semplifica per 4, diventa 25/7);

= radice quadrata[(25/7) x (7/15) x (1/ 25) x (3/5)] =

25/7 x 7/15 = 5 x 1 /(1 x 3) = 5/3.

= radice quadrata[(5/3) x (1/ 25) x (3/5)] =

5/3 x 1/25 = 1/15;   1/15 x 3/5 = 1 / (5 x 5) = 1/25;

= radice quadrata[1/25] = 1/5.

Ciao @miry27

115)

$\small \sqrt{\dfrac{10^2}{28} : \dfrac{15}{7} : 25 : \dfrac{5}{3}}=$

$\small =\sqrt{\dfrac{\cancel{100}^{25}}{\cancel{28}_7}·\dfrac{7}{15}·\dfrac{1}{25}·\dfrac{3}{5}}=$

semplifica in croce, 25 con 25, 7 con 7 e 3 con 15:

$\small =\sqrt{\dfrac{\cancel{25}^1}{\cancel7_1}·\dfrac{\cancel7^1}{\cancel{15}_5}·\dfrac{1}{\cancel{25}_1}·\dfrac{\cancel3^1}{5}}=$

$\small =\sqrt{\dfrac{1}{5}·\dfrac{1}{5}}=$

$\small =\sqrt{\dfrac{1}{25}} = \dfrac{1}{5}$