Question

Вычислите:
$sqrt{15- 4sqrt{14} } - sqrt{15+4 sqrt{14} }$

Answer 1

$sqrt{15-4 sqrt{14} } - sqrt{15+4 sqrt{14} } = sqrt{15-4 sqrt{2}* sqrt{7} } - sqrt{15+4 sqrt{2}* sqrt{7} } =\ = sqrt{(2 sqrt{2}- sqrt{7} )^2 } - sqrt{(2 sqrt{2}+ sqrt{7} )^2 } =|2 sqrt{2}- sqrt{7} |-|2 sqrt{2}+ sqrt{7} |=\ = 2 sqrt{2}- sqrt{7} -2 sqrt{2}- sqrt{7} =-2 sqrt{7}$