==========================================================
$\sqrt{1+\left(\dfrac{3}{5}+\dfrac{7}{10}\right) : \dfrac{13}{20}-\dfrac{3}{10}×\dfrac{\cancel{30}^{15}}{\cancel4_2}+\left(\dfrac{5}{2}+\dfrac{3}{4}\right)}=$
$=\sqrt{1+\left(\dfrac{6+7}{10}\right)×\dfrac{20}{13}-\dfrac{3}{\cancel{10}_2}×\dfrac{\cancel{15}^3}{2}+\left(\dfrac{10+3}{4}\right)}=$
$=\sqrt{1+\dfrac{\cancel{13}^1}{\cancel{10}_1}×\dfrac{\cancel{20}^2}{\cancel{13}_1}-\dfrac{3}{2}×\dfrac{3}{2}+\dfrac{13}{4}}=$
$=\sqrt{1+\dfrac{1}{1}×\dfrac{2}{1}-\dfrac{9}{4}+\dfrac{13}{4}}=$
$= \sqrt{1+2-\dfrac{9}{4}+\dfrac{13}{4}}=$
$=\sqrt{\dfrac{4+8-9+13}{4}}$
$=\sqrt{\dfrac{\cancel{16}^4}{\cancel4_1}}=$
$= \sqrt4=$
$=2$