Question

вычислите √(12-√13)² + √(3-√13)²

Answer 1

$sqrt{ {(12 - sqrt{13} )}^{2} } + sqrt{ {(3 - sqrt{13} )}^{2} } = \ 12 - sqrt{13 } + sqrt{13} - 3 = 9$

Answer 2

$boxed {sqrt{a^2}=|a|=left { {{a; ,; esli; ageq 0; ,} atop {-a; ,; esli; a<0; .}} right. }\\\sqrt{12-sqrt{13}}+sqrt{3-sqrt{13}}=|12-sqrt{13}|+|3-sqrt{13}|=\\\star ; ; 3<sqrt{13}<4,; t.k.; 13>3^2=9; ; ,; 13<4^2=16; ; Rightarrow \\(12-sqrt{13})>0; ; i; ; |12-sqrt{13}|=12-sqrt{13}; ;\\(3-sqrt{13})<0; ; Rightarrow ; ; |3-sqrt{13}|=-(3-sqrt{13})=sqrt{13}-3; ; star \\\=12-sqrt{13}+sqrt{13}-3=12-3=9$