Riješi (54002341048623*(4+8))/(sqrt{88247711001123870*4287)+84/81}

$$\frac { ( 54002341048623 \cdot ( 4 + 8 ) ) } { ( \sqrt { 88247711001123870 \cdot 4287 } ) + \frac { 84 } { 81 } }$$

Izračunaj

$$\frac{708618719240031006\sqrt{42035326340202003410}}{137896888059032672186113}-\frac{34993516999507704}{19699555437004667455159}\approx 33316,959958538$$

Koraci rješenja

Dodajte 4 broju 8 da biste dobili 12.

$$\frac{54002341048623\times 12}{\sqrt{88247711001123870\times 4287}+\frac{84}{81}}$$

Pomnožite 54002341048623 i 12 da biste dobili 648028092583476.

$$\frac{648028092583476}{\sqrt{88247711001123870\times 4287}+\frac{84}{81}}$$

Pomnožite 88247711001123870 i 4287 da biste dobili 378317937061818030690.

$$\frac{648028092583476}{\sqrt{378317937061818030690}+\frac{84}{81}}$$

Rastavite 378317937061818030690=3^{2}\times 42035326340202003410 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{3^{2}\times 42035326340202003410} kao umnožak kvadrata korijena \sqrt{3^{2}}\sqrt{42035326340202003410}. Izračunajte kvadratni korijen od 3^{2}.

$$\frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{84}{81}}$$

Skratite razlomak \frac{84}{81} na najmanje vrijednosti tako da izlučite i poništite 3.

$$\frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{28}{27}}$$

Racionalizirajte nazivnik \frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{28}{27}} množenje brojnik i nazivnik 3\sqrt{42035326340202003410}-\frac{28}{27}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\left(3\sqrt{42035326340202003410}+\frac{28}{27}\right)\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}$$

Razmotrite \left(3\sqrt{42035326340202003410}+\frac{28}{27}\right)\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right). Umnožak se može pretvoriti u razliku kvadrata pomoću sljedećeg pravila: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\left(3\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Proširivanje broja \left(3\sqrt{42035326340202003410}\right)^{2}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{3^{2}\left(\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Izračunajte koliko je 2 na 3 da biste dobili 9.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{9\left(\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Kvadrat od \sqrt{42035326340202003410} je 42035326340202003410.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{9\times 42035326340202003410-\left(\frac{28}{27}\right)^{2}}$$

Pomnožite 9 i 42035326340202003410 da biste dobili 378317937061818030690.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{378317937061818030690-\left(\frac{28}{27}\right)^{2}}$$

Izračunajte koliko je 2 na \frac{28}{27} da biste dobili \frac{784}{729}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{378317937061818030690-\frac{784}{729}}$$

Pretvorite 378317937061818030690 u razlomak \frac{275793776118065344373010}{729}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344373010}{729}-\frac{784}{729}}$$

Budući da \frac{275793776118065344373010}{729} i \frac{784}{729} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344373010-784}{729}}$$

Oduzmite 784 od 275793776118065344373010 da biste dobili 275793776118065344372226.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344372226}{729}}$$

Podijelite 648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right) s \frac{275793776118065344372226}{729} da biste dobili \frac{236206239746677002}{137896888059032672186113}\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right).

$$\frac{236206239746677002}{137896888059032672186113}\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)$$

Koristite svojstvo distributivnosti da biste pomnožili \frac{236206239746677002}{137896888059032672186113} s 3\sqrt{42035326340202003410}-\frac{28}{27}.

$$\frac{236206239746677002}{137896888059032672186113}\times 3\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Izrazite \frac{236206239746677002}{137896888059032672186113}\times 3 kao jedan razlomak.

$$\frac{236206239746677002\times 3}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Pomnožite 236206239746677002 i 3 da biste dobili 708618719240031006.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Pomnožite \frac{236206239746677002}{137896888059032672186113} i -\frac{28}{27} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002\left(-28\right)}{137896888059032672186113\times 27}$$

Izvedite množenje u razlomku \frac{236206239746677002\left(-28\right)}{137896888059032672186113\times 27}.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{-6613774712906956056}{3723215977593882149025051}$$

Skratite razlomak \frac{-6613774712906956056}{3723215977593882149025051} na najmanje vrijednosti tako da izlučite i poništite 189.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}-\frac{34993516999507704}{19699555437004667455159}$$

Faktor

$$\frac{8748379249876926 {(81 \sqrt{42035326340202003410} - 28)}}{137896888059032672186113} = 33316\frac{1,3237529501491374 \times 10^{23}}{1,3789688805903266 \times 10^{23}} = 33316,9599585377$$