Question

calcule raiz quadrada de (2 - raiz quadrada de 5)^2 -raiz quadrada de 5?

Answer 1

$\displaystyle \sqrt{2-\sqrt{5}}^2-\sqrt{5}=x$
$\displaystyle i)~~~\sqrt{2-\sqrt{5}}^2-\sqrt{5}=\left(\left(2-(5)^{\frac{1}{2}}\right)^{\frac{1}{2}}\right)^2-(5)^{ \frac{1}{2} }=x\\\\ii)~~\left(2-5^{\frac{1}{2}}\right)^{\frac{2}{2}}-5^{\frac{1}{2}}=x\\\\iii)~~~2-\sqrt5-\sqrt5=x\\\\iv)~~~2-2\sqrt{5}=x\\\\v)~~~~\boxed{x=2-2\sqrt5}$
lembrando que:
$\displaystyle \sqrt[b]{a^c}=a^{\frac{c}{b}}\\\\(a^b)^c=a^{b\cdot c}$