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

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