Grazie 🌹

√2/15+1/3-1/6+7/10

√(2+5)/15-1/6+7/10

√(14-5)/30+7/10

√(9+21)/30 

√30/30 = 1 

√((10-3)/6+5/12*8/15)/2

√(7/6+5/12*8/15)/2

√(7/6+2/9)/2

√(21+4)/18/2 = 

√25/36 = 5/6 

179/1)

$\small \sqrt{\dfrac{2}{9}×\dfrac{3}{5}+\dfrac{1}{3}-\dfrac{4}{9} : \dfrac{8}{3}+\dfrac{7}{10}}=$

$\small =\sqrt{\dfrac{2}{\cancel9_3}×\dfrac{\cancel3^1}{5}+\dfrac{1}{3}-\dfrac{4}{9}×\dfrac{3}{8}+\dfrac{7}{10}}=$

$\small =\sqrt{\dfrac{2}{3}×\dfrac{1}{5}+\dfrac{1}{3}-\dfrac{\cancel4^1}{\cancel9_3}×\dfrac{\cancel3^1}{\cancel8_2}+\dfrac{7}{10}}=$

$\small =\sqrt{\dfrac{2}{15}+\dfrac{1}{3}-\dfrac{1}{3}×\dfrac{1}{2}+\dfrac{7}{10}}=$

$\small =\sqrt{\dfrac{2}{15}+\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{7}{10}}=$

$\small =\sqrt{\dfrac{4+10-5+21}{30}}=$

$\small =\sqrt{\dfrac{\cancel{30}^1}{\cancel{30}_1}}= \sqrt1 = 1$

179/2)

$\small \sqrt{\left(\dfrac{5}{3}-\dfrac{1}{2}+\dfrac{5}{12}×\dfrac{8}{15}\right) : \dfrac{1}{2}}= $

$\small = \sqrt{\left(\dfrac{5}{3}-\dfrac{1}{2}+\dfrac{\cancel5^1}{\cancel{12}_3}×\dfrac{\cancel8^2}{\cancel{15}_3}\right)×2}= $

$\small = \sqrt{\left(\dfrac{5}{3}-\dfrac{1}{2}+\dfrac{1}{3}×\dfrac{2}{3}\right)×2}= $

$\small = \sqrt{\left(\dfrac{5}{3}-\dfrac{1}{2}+\dfrac{2}{9}\right)×2}= $

$\small = \sqrt{\left(\dfrac{30-9+4}{18}\right)×2}= $

$\small = \sqrt{\dfrac{25}{\cancel{18}_9}×\cancel2^1}= $

$\small = \sqrt{\dfrac{25}{9}}= \dfrac{5}{3}$