Răspuns: [tex]\purple{\bf~\dfrac{22}{3}~}[/tex]
Explicație pas cu pas:
[tex]\bf \sqrt{53,(7)} =\sqrt{\dfrac{537 - 53}{9}} =\sqrt{\dfrac{484}{9}}=\sqrt{\dfrac{2^{2}\cdot11^{2}}{3^{2}}}=[/tex]
[tex]\bf \sqrt{\bigg( \dfrac{2\cdot11}{3}\bigg)^{2}}= \sqrt{\bigg( \dfrac{22}{3}\bigg)^{2}}=\red{\boxed{\bf~\dfrac{22}{3}~}}[/tex]
484 | 2
242 | 2
121 | 11
11 | 11
1 | 1 ⇒ 484 = 2² × 11²
