Question

√(11-4√7) + √(16 - 6√7)

Answer 1

$\sqrt{11-4 \sqrt{7} } + \sqrt{16-6 \sqrt{7} } = \sqrt{7+4-4 \sqrt{7} } + \sqrt{9+7-6 \sqrt{7} }=$

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

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

$=\sqrt{7}-2+3-\sqrt{7}=1$