Question

Se a = 0,666... e b = 0,111..., então a√b é igual a____________________

Answer 1

$\mathtt{a=0,666.... \times10}\\\mathtt{10a=6,666... }$

$\mathtt{-\underline{\begin{cases}10a=6,666... \\a=0,666... \end{cases}}}$

$\mathtt{9a=6}\\\mathtt{a=\dfrac{6\div3}{9\div3}=\dfrac{2}{3}}$

$\mathtt{b=0,111.... \times10}\\\mathtt{10b=1,111...}$

$\mathtt{-\underline{\begin{cases}10b=1,111... \\b=0,111... \end{cases}}}$

$\mathtt{9b=1}\\\mathtt{b=\dfrac{1}{9}}$

$\mathtt{a.\sqrt{b}=\dfrac{2}{3}.\sqrt{\dfrac{1}{9}}}\\\mathtt{\dfrac{2}{3}.\dfrac{1}{3}}$

$\huge\boxed{\boxed{\mathtt{a.\sqrt{b}=\dfrac{2}{9}}}}$

Answer 2

a=0,666..= 6/9 = 2/3

b=0,111..= 1/9

a.√b = 2/3. √1/9 = 2/3. 1/3 = 2/9 ✓