0,(3) se inmulteste cu √21
Pentru a-l introduce pe 0,(3) sub radical il transformam in fractie
apoi il ridicam la patrat.
.
[tex]\displaystyle\bf\\0,3=\frac{~~3^{(3}}{9}=\frac{1}{3}\\\\\left(\frac{1}{3}\right)^2=\frac{1}{9}\\\\\implies~\sqrt\frac{1}{9}}=\frac{1}{3}\\\\\implies~0,(3)\cdot\sqrt{21}=\frac{1}{3}\cdot\sqrt{21}=\sqrt\frac{1}{9}}\cdot\sqrt{21}= \sqrt{\frac{1}{9}\cdot21}=\sqrt\frac{21}{9}=\boxed{\bf\sqrt\frac{7}{3}}\\\\Am~folosit~formula:~~~\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}[/tex]