Question

raiz quadrada de 2/0,666...

Answer 1

Vamos achar a fração geratriz de 0,666...:

$x=0,666...\\\\10\cdot x=10\cdot0,666...\\\\10x=6,666...\\\\10x=6+0,666...\\\\10x=6+x\\\\9x=6\\\\x=\dfrac{6}{9}~~~\therefore~~~x=\dfrac{2}{3}$
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$\sqrt{\dfrac{2}{0,666...}}=\sqrt{\dfrac{2}{(\frac{2}{3})}}}\\\\\\\sqrt{\dfrac{2}{0,666...}}=\sqrt{2\cdot\dfrac{3}{2}}\\\\\\\boxed{\boxed{\sqrt{\dfrac{2}{0,666...}}=\sqrt{3}}}$