Riješi 12/sqrt{1-frac{100{910^16}}}

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

Izračunaj

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

Koraci rješenja

Izračunajte koliko je 16 na 10 da biste dobili 10000000000000000.

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

Pomnožite 9 i 10000000000000000 da biste dobili 90000000000000000.

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

Skratite razlomak \frac{100}{90000000000000000} na najmanje vrijednosti tako da izlučite i poništite 100.

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

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

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

Budući da \frac{900000000000000}{900000000000000} i \frac{1}{900000000000000} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Oduzmite 1 od 900000000000000 da biste dobili 899999999999999.

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

Ponovno napišite kvadratni korijen dijeljenja \sqrt{\frac{899999999999999}{900000000000000}} kao dijeljenje kvadrata korijena \frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}.

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

Izračunajte 2. korijen od 900000000000000 da biste dobili 30000000.

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

Podijelite 12 s \frac{\sqrt{899999999999999}}{30000000} tako da pomnožite 12 s brojem recipročnim broju \frac{\sqrt{899999999999999}}{30000000}.

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

Racionalizirajte nazivnik \frac{12\times 30000000}{\sqrt{899999999999999}} množenje brojnik i nazivnik \sqrt{899999999999999}.

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

Kvadrat od \sqrt{899999999999999} je 899999999999999.

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

Pomnožite 12 i 30000000 da biste dobili 360000000.

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