Question

calculați ✓53,(7)
ajutor​

Answer 1

Răspuns:

$53,(7)=\frac{537-53}{9} =\frac{484}{9} \\\\\sqrt{\frac{484}{9} } =\frac{22}{3}$

Answer 2

Răspuns: $\purple{\bf~\dfrac{22}{3}~}$

Explicație pas cu pas:

$\bf \sqrt{53,(7)} =\sqrt{\dfrac{537 - 53}{9}} =\sqrt{\dfrac{484}{9}}=\sqrt{\dfrac{2^{2}\cdot11^{2}}{3^{2}}}=$

$\bf \sqrt{\bigg( \dfrac{2\cdot11}{3}\bigg)^{2}}= \sqrt{\bigg( \dfrac{22}{3}\bigg)^{2}}=\red{\boxed{\bf~\dfrac{22}{3}~}}$

484 | 2

242 | 2

 121 | 11

   11 | 11

    1 | 1    ⇒ 484 = 2² × 11²