Question

Вычислите
$sqrt{28-10 sqrt{3}} + sqrt{28+10 sqrt{3}}$
Должно получится 10

Answer 1

$(sqrt{a})^2=|a|$


$sqrt{28-10sqrt{3}}+sqrt{28+10sqrt{3}}=$$= sqrt{5^2+2cdot5cdotsqrt{3}+(sqrt{3})^2}+sqrt{5^2-2cdot5cdotsqrt{3}+(sqrt{3})^2}=$$=sqrt{(5+sqrt{3})^2}+sqrt{(5-sqrt{3})^2}=|5+sqrt{3}|+|5-sqrt{3}|=5+sqrt3+5-sqrt3$$=10$.