Riješi 12/sqrt{1-frac{100{910^16}}}

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

Procijeni

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

Koraci za rješenje

Izračunajte 10 stepen od 16 i dobijte 10000000000000000.

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

Pomnožite 9 i 10000000000000000 da biste dobili 90000000000000000.

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

Svedite razlomak \frac{100}{90000000000000000} na najprostije elemente rastavlјanjem i kraćenjem 100.

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

Konvertirajte 1 u razlomak \frac{900000000000000}{900000000000000}.

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

Pošto \frac{900000000000000}{900000000000000} i \frac{1}{900000000000000} imaju isti imenilac, oduzmite ih tako što ćete oduzeti njihove brojioce.

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

Oduzmite 1 od 900000000000000 da biste dobili 899999999999999.

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

Ponovo napišite kvadratni korijen dijeljenja \sqrt{\frac{899999999999999}{900000000000000}} kao dijeljenje kvadratnih korijena \frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}.

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

Izračunajte kvadratni koren od 900000000000000 i dobijte 30000000.

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

Podijelite 12 sa \frac{\sqrt{899999999999999}}{30000000} tako što ćete pomnožiti 12 recipročnom vrijednošću od \frac{\sqrt{899999999999999}}{30000000}.

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

Racionalizirajte imenilac broja \frac{12\times 30000000}{\sqrt{899999999999999}} tako što ćete pomnožiti brojilac i imenilac sa \sqrt{899999999999999}.

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

Kvadrat broja \sqrt{899999999999999} je 899999999999999.

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

Pomnožite 12 i 30000000 da biste dobili 360000000.

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