Question

Como resolver √(1-√3)^2

Answer 1

$\Large\boxed{\begin{array}{l}\sf\sqrt{(1-\sqrt{3})^2}=\sqrt{1-2\sqrt{3}+3}\\\sf=\sqrt{4-2\sqrt{3}}=\sqrt{4-\sqrt{12}}\\\underline{\rm Radical\,Duplo}\\\sf\sqrt{A\pm\sqrt{B}}=\sqrt{\dfrac{A+C}{2}}\pm\sqrt{\dfrac{A-C}{2}}\\\sf onde~C=\sqrt{A^2-B}.\\\sf \sqrt{4-\sqrt{12}}\implies A=4~~B=12\\\sf C=\sqrt{A^2-B}=\sqrt{16-12}=\sqrt{4}=2\\\sf \sqrt{4-\sqrt{12}}=\sqrt{\dfrac{4+2}{2}}-\sqrt{\dfrac{4-2}{2}}\\\sf\sqrt{4-\sqrt{12}}=\sqrt{\dfrac{6}{2}}-\sqrt{\dfrac{2}{2}}\\\\\sf \sqrt{4-\sqrt{12}}=\sqrt{3}-1\\\sf portanto\\\sf \sqrt{(1-\sqrt{3})^2}=\sqrt{3}-1\end{array}}$