Question

спростить виражение
√((√3 – 4)^2 )+√(28-10√3)

Answer 1

√((√3 – 4)²)+√(28-10√3)= √((√3 – 4)²)+√(25-10√3+3)=

= √((√3 – 4)² )+√(√5- √3)²= √3 – 4+√5- √3 =√5 - 4

Answer 2

$\sqrt{(\sqrt3-4)^2}+\sqrt{28-10\sqrt3}=|\underbrace {\sqrt3-4}_{\ \textless \ 0}|+\sqrt{25-2\cdot 5\sqrt3+3}=\\\\=-(\sqrt3-4)+\sqrt{(5-\sqrt3)^2}=4-\sqrt3+|\underbrace {5-\sqrt3}_{\ \textgreater \ 0}|=\\\\=4-\sqrt3+5-\sqrt3=9-2\sqrt3$