Question

Ребята, помогите пожалуйста!!!

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

Найдите значение выражения!!

Answer 1

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