Question

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

Answer 1

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

По действиям:

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

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

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

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

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