Cho các số: \(\sqrt 6 ;\,\, - 3;\,\,\sqrt {49} ;\,\, - \frac{2}{5};\,\,\sqrt 7 ;\,\, - \sqrt {12} ;\,\, - \sqrt {\frac{9}{{16}}} \). Có bao nhiêu số vô tỉ trong các số đã cho?

Ta có: \(1\frac{4}{9} - \frac{1}{{25}}:\left( {x + \frac{1}{4}} \right) = \sqrt {1\frac{7}{9}} \)

\(\frac{{13}}{9} - \frac{1}{{25}}:\left( {x + \frac{1}{4}} \right) = \sqrt {\frac{{16}}{9}} \)

\(\frac{{13}}{9} - \frac{1}{{25}}:\left( {x + \frac{1}{4}} \right) = \sqrt {{{\left( {\frac{4}{3}} \right)}^2}} \)

\(\frac{{13}}{9} - \frac{1}{{25}}:\left( {x + \frac{1}{4}} \right) = \frac{4}{3}\)

\(\frac{1}{{25}}:\left( {x + \frac{1}{4}} \right) = \frac{{13}}{9} - \frac{4}{3}\)

\(\frac{1}{{25}}:\left( {x + \frac{1}{4}} \right) = \frac{1}{9}\)

\(x + \frac{1}{4} = \frac{1}{{25}}:\frac{1}{9}\)

\(x + \frac{1}{4} = \frac{9}{{25}}\)

\(x = \frac{9}{{25}} - \frac{1}{4}\)

\(x = \frac{{11}}{{100}}\)

\(x = 0,11\).

Vậy \(x = 0,11\).