Question

Найдите целое число - значение выражения

√(7-4√3) +√(4-2√3)

Answer 1

$sqrt{4+3-4sqrt3}+sqrt{1+3-2sqrt3}=\ sqrt{(2-sqrt3)^2}+sqrt{(1-sqrt3)^2}=\ |2-sqrt3|+|1-sqrt3|=\ 2-sqrt3-1+sqrt3=1$

Answer 2

$sqrt{7-4sqrt{3}}+sqrt{4-2sqrt{3}}=\ sqrt{4-4sqrt{3}+3}+sqrt{1-2sqrt{3}+3}=\ sqrt{2^2-2*2*sqrt{3}+(sqrt{3})^2}+sqrt{1^2-2*1*sqrt{3}+(sqrt{3})^2}=\ sqrt{(2-sqrt{3})^2}+sqrt{(1-sqrt{3})^2}=\ |2-sqrt{3}|+|1-sqrt{3}|=2-sqrt{3}-1+sqrt{3}=1$