Rešite 12/sqrt{1-frac{100{910^16}}}

$$\frac{ 12 }{ \sqrt{ 1- \frac{ 100 }{ 9 { 10 }^{ 16 } } } }$$

Ovrednoti

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}\approx 12$$

Koraki rešitve

Izračunajte potenco 10 števila 16, da dobite 10000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{9\times 10000000000000000}}}$$

Pomnožite 9 in 10000000000000000, da dobite 90000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{90000000000000000}}}$$

Zmanjšajte ulomek \frac{100}{90000000000000000} na najmanjši imenovalec tako, da izpeljete in okrajšate 100.

$$\frac{12}{\sqrt{1-\frac{1}{900000000000000}}}$$

Pretvorite 1 v ulomek \frac{900000000000000}{900000000000000}.

$$\frac{12}{\sqrt{\frac{900000000000000}{900000000000000}-\frac{1}{900000000000000}}}$$

Ker \frac{900000000000000}{900000000000000} in \frac{1}{900000000000000} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{12}{\sqrt{\frac{900000000000000-1}{900000000000000}}}$$

Odštejte 1 od 900000000000000, da dobite 899999999999999.

$$\frac{12}{\sqrt{\frac{899999999999999}{900000000000000}}}$$

Znova napišite kvadratni koren deljenja \sqrt{\frac{899999999999999}{900000000000000}} kot deljenje kvadratnih korenov \frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}.

$$\frac{12}{\frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}}$$

Izračunajte kvadratni koren števila 900000000000000 in dobite 30000000.

$$\frac{12}{\frac{\sqrt{899999999999999}}{30000000}}$$

Delite 12 s/z \frac{\sqrt{899999999999999}}{30000000} tako, da pomnožite 12 z obratno vrednostjo \frac{\sqrt{899999999999999}}{30000000}.

$$\frac{12\times 30000000}{\sqrt{899999999999999}}$$

Racionalizirajte imenovalec \frac{12\times 30000000}{\sqrt{899999999999999}} tako, da pomnožite števec in imenovalec s \sqrt{899999999999999}.

$$\frac{12\times 30000000\sqrt{899999999999999}}{\left(\sqrt{899999999999999}\right)^{2}}$$

Kvadrat vrednosti \sqrt{899999999999999} je 899999999999999.

$$\frac{12\times 30000000\sqrt{899999999999999}}{899999999999999}$$

Pomnožite 12 in 30000000, da dobite 360000000.

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}$$