Issolvi {left(sqrt{1/9+frac{6/18}}{{left(5-23/3right)}^2}right)}^3

$${ \left( \frac{ \sqrt{ \frac{ 1 }{ 9 } + \frac{ 6 }{ 18 } } }{ { \left(5- \frac{ 23 }{ 3 } \right) }^{ 2 } } \right) }^{ 3 }$$

Evalwa

$$\frac{27}{32768}=0.000823975$$

Passi tas-Soluzzjonijiet

Naqqas il-frazzjoni \frac{6}{18} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 6.

$$\left(\frac{\sqrt{\frac{1}{9}+\frac{1}{3}}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

Żid \frac{1}{9} u \frac{1}{3} biex tikseb \frac{4}{9}.

$$\left(\frac{\sqrt{\frac{4}{9}}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \frac{4}{9} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{4}}{\sqrt{9}}. Ħu r-radiċi kwadrata tan-numeratur u d-denominatur.

$$\left(\frac{\frac{2}{3}}{\left(5-\frac{23}{3}\right)^{2}}\right)^{3}$$

Naqqas \frac{23}{3} minn 5 biex tikseb -\frac{8}{3}.

$$\left(\frac{\frac{2}{3}}{\left(-\frac{8}{3}\right)^{2}}\right)^{3}$$

Ikkalkula -\frac{8}{3} bil-power ta' 2 u tikseb \frac{64}{9}.

$$\left(\frac{\frac{2}{3}}{\frac{64}{9}}\right)^{3}$$

Iddividi \frac{2}{3} b'\frac{64}{9} billi timmultiplika \frac{2}{3} bir-reċiproku ta' \frac{64}{9}.

$$\left(\frac{2}{3}\times \frac{9}{64}\right)^{3}$$

Immultiplika \frac{2}{3} u \frac{9}{64} biex tikseb \frac{3}{32}.

$$\left(\frac{3}{32}\right)^{3}$$

Ikkalkula \frac{3}{32} bil-power ta' 3 u tikseb \frac{27}{32768}.

$$\frac{27}{32768}$$

Fattur

$$\frac{3 ^ {3}}{2 ^ {15}} = 0.000823974609375$$