Question

Вычислите : √(7+4√3) + √(7-4√3)

Answer 1

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