Question

Ребята, помогите пожалуйста!!!

$\sqrt{52-10\sqrt{27} } - \sqrt{52+10\sqrt{27} }$

Найдите значение выражения!!

Answer 1

$\sqrt{52-10\sqrt{27} } - \sqrt{52+10\sqrt{27} }=\\\\\sqrt{27-10\sqrt{27} +25} - \sqrt{27+10\sqrt{27}+25}=\\\\\sqrt{(\sqrt{27})^2-10\sqrt{27} +5^2} - \sqrt{(\sqrt{27})^2+10\sqrt{27}+5^2}=\\\\\sqrt{(\sqrt{27}-5)^2} - \sqrt{(\sqrt{27}+5)^2}=\\\\|\sqrt{27}-5| - |\sqrt{27}+5|=\sqrt{27}-5 - \sqrt{27}-5=-10$