Question

cum se calculează
$\sqrt{1virgula(7)}$
​

Answer 1

Explicație pas cu pas:

$\sqrt{1,(7)} = \sqrt{ \dfrac{17 - 1}{9} } = \sqrt{ \dfrac{16}{9} } = \sqrt{ \dfrac{ {4}^{2} }{ {3}^{2} } } = \dfrac{4}{3} = 1\dfrac{1}{3} = 1,(3)$

$\sqrt{5,(4)} = \sqrt{ \dfrac{54 - 5}{9} } = \sqrt{ \dfrac{49}{9} } = \sqrt{ \dfrac{ {7}^{2} }{ {3}^{2} } } = \dfrac{7}{3} = 2\dfrac{1}{3} = 2,(3)$

$\sqrt{7,(1)} = \sqrt{ \dfrac{71 - 7}{9} } = \sqrt{ \dfrac{64}{9} } = \sqrt{ \dfrac{ {8}^{2} }{ {3}^{2} } } = \dfrac{8}{3} = 2\dfrac{2}{3} = 2,(6)$

$\sqrt{0,13(4)} = \sqrt{ \dfrac{134 - 13}{900} } = \sqrt{ \dfrac{121}{900} } = \sqrt{ \dfrac{ {11}^{2} }{ {30}^{2} } } = \dfrac{11}{30} = \dfrac{33}{90} = 0,3(6)$

$\sqrt{0,32(1)} = \sqrt{ \dfrac{321 - 32}{900} } = \sqrt{ \dfrac{289}{900} } = \sqrt{ \dfrac{ {17}^{2} }{ {30}^{2} } } = \dfrac{17}{30} = \dfrac{51}{90} = 0,5(6)$