Question

Знайдіть значення виразу$sqrt{52-10sqrt{27} }$-$sqrt{52+10} sqrt{27}$
Помогитє срочно!!!!!

Answer 1

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

По действиям:

$1)sqrt{52-10sqrt{27}}=sqrt{27-10sqrt{27}+25}=$

$=sqrt{(sqrt{27})^2-2*sqrt{27}*5+5^2}=sqrt{(sqrt{27}-5)^2}=sqrt{27}-5$

$2)sqrt{52+10sqrt{27}}=sqrt{27+10sqrt{27}+25}=$

$=sqrt{(sqrt{27})^2+2*sqrt{27}*5+5^2}=sqrt{(sqrt{27}+5)^2}=sqrt{27}+5$

$3)sqrt{27}-5-(sqrt{27}+5)=sqrt{27}-5-sqrt{27}-5=-10$