Riješi sqrt{frac{5sqrt{5}+2sqrt{29}+sqrt{41}}{2}*frac{-5sqrt{5}+2sqrt{29}+sqrt{41}}{2}*frac{5sqrt{5}-2sqrt{29}+sqrt{41}}{2}*frac{5sqrt{5}+2sqrt{29}-sqrt{41}}{2}}=

$$\sqrt{ \frac{ 5 \sqrt{ 5 } +2 \sqrt{ 29 } + \sqrt{ 41 } }{ 2 } \times \frac{ -5 \sqrt{ 5 } +2 \sqrt{ 29 } + \sqrt{ 41 } }{ 2 } \times \frac{ 5 \sqrt{ 5 } -2 \sqrt{ 29 } + \sqrt{ 41 } }{ 2 } \times \frac{ 5 \sqrt{ 5 } +2 \sqrt{ 29 } - \sqrt{ 41 } }{ 2 } } =$$

Izračunaj

$$15\sqrt{5}\approx 33,541019662$$

Koraci rješenja

Pomnožite \frac{5\sqrt{5}+2\sqrt{29}+\sqrt{41}}{2} i \frac{-5\sqrt{5}+2\sqrt{29}+\sqrt{41}}{2} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

$$\sqrt{\frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)}{2\times 2}\times \frac{5\sqrt{5}-2\sqrt{29}+\sqrt{41}}{2}\times \frac{5\sqrt{5}+2\sqrt{29}-\sqrt{41}}{2}}$$

Pomnožite \frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)}{2\times 2} i \frac{5\sqrt{5}-2\sqrt{29}+\sqrt{41}}{2} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

$$\sqrt{\frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)}{2\times 2\times 2}\times \frac{5\sqrt{5}+2\sqrt{29}-\sqrt{41}}{2}}$$

Pomnožite \frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)}{2\times 2\times 2} i \frac{5\sqrt{5}+2\sqrt{29}-\sqrt{41}}{2} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

$$\sqrt{\frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{2\times 2\times 2\times 2}}$$

Pomnožite 2 i 2 da biste dobili 4.

$$\sqrt{\frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{4\times 2\times 2}}$$

Pomnožite 4 i 2 da biste dobili 8.

$$\sqrt{\frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{8\times 2}}$$

Pomnožite 8 i 2 da biste dobili 16.

$$\sqrt{\frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza 5\sqrt{5}+2\sqrt{29}+\sqrt{41} sa svakim dijelom izraza -5\sqrt{5}+2\sqrt{29}+\sqrt{41}.

$$\sqrt{\frac{\left(-25\left(\sqrt{5}\right)^{2}+10\sqrt{29}\sqrt{5}+5\sqrt{5}\sqrt{41}-10\sqrt{5}\sqrt{29}+4\left(\sqrt{29}\right)^{2}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kvadrat od \sqrt{5} je 5.

$$\sqrt{\frac{\left(-25\times 5+10\sqrt{29}\sqrt{5}+5\sqrt{5}\sqrt{41}-10\sqrt{5}\sqrt{29}+4\left(\sqrt{29}\right)^{2}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Pomnožite -25 i 5 da biste dobili -125.

$$\sqrt{\frac{\left(-125+10\sqrt{29}\sqrt{5}+5\sqrt{5}\sqrt{41}-10\sqrt{5}\sqrt{29}+4\left(\sqrt{29}\right)^{2}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Da biste pomnožite \sqrt{29} i \sqrt{5}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{\left(-125+10\sqrt{145}+5\sqrt{5}\sqrt{41}-10\sqrt{5}\sqrt{29}+4\left(\sqrt{29}\right)^{2}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Da biste pomnožite \sqrt{5} i \sqrt{41}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{\left(-125+10\sqrt{145}+5\sqrt{205}-10\sqrt{5}\sqrt{29}+4\left(\sqrt{29}\right)^{2}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Da biste pomnožite \sqrt{5} i \sqrt{29}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{\left(-125+10\sqrt{145}+5\sqrt{205}-10\sqrt{145}+4\left(\sqrt{29}\right)^{2}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kombinirajte 10\sqrt{145} i -10\sqrt{145} da biste dobili 0.

$$\sqrt{\frac{\left(-125+5\sqrt{205}+4\left(\sqrt{29}\right)^{2}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kvadrat od \sqrt{29} je 29.

$$\sqrt{\frac{\left(-125+5\sqrt{205}+4\times 29+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Pomnožite 4 i 29 da biste dobili 116.

$$\sqrt{\frac{\left(-125+5\sqrt{205}+116+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Dodajte -125 broju 116 da biste dobili -9.

$$\sqrt{\frac{\left(-9+5\sqrt{205}+2\sqrt{29}\sqrt{41}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Da biste pomnožite \sqrt{29} i \sqrt{41}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{\left(-9+5\sqrt{205}+2\sqrt{1189}-5\sqrt{41}\sqrt{5}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Da biste pomnožite \sqrt{41} i \sqrt{5}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{\left(-9+5\sqrt{205}+2\sqrt{1189}-5\sqrt{205}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kombinirajte 5\sqrt{205} i -5\sqrt{205} da biste dobili 0.

$$\sqrt{\frac{\left(-9+2\sqrt{1189}+2\sqrt{41}\sqrt{29}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Da biste pomnožite \sqrt{41} i \sqrt{29}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{\left(-9+2\sqrt{1189}+2\sqrt{1189}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kombinirajte 2\sqrt{1189} i 2\sqrt{1189} da biste dobili 4\sqrt{1189}.

$$\sqrt{\frac{\left(-9+4\sqrt{1189}+\left(\sqrt{41}\right)^{2}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kvadrat od \sqrt{41} je 41.

$$\sqrt{\frac{\left(-9+4\sqrt{1189}+41\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Dodajte -9 broju 41 da biste dobili 32.

$$\sqrt{\frac{\left(32+4\sqrt{1189}\right)\left(5\sqrt{5}-2\sqrt{29}+\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza 32+4\sqrt{1189} sa svakim dijelom izraza 5\sqrt{5}-2\sqrt{29}+\sqrt{41}.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}+32\sqrt{41}+20\sqrt{5}\sqrt{1189}-8\sqrt{29}\sqrt{1189}+4\sqrt{1189}\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Da biste pomnožite \sqrt{5} i \sqrt{1189}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}+32\sqrt{41}+20\sqrt{5945}-8\sqrt{29}\sqrt{1189}+4\sqrt{1189}\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Rastavite 1189=29\times 41 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{29\times 41} kao umnožak kvadrata korijena \sqrt{29}\sqrt{41}.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}+32\sqrt{41}+20\sqrt{5945}-8\sqrt{29}\sqrt{29}\sqrt{41}+4\sqrt{1189}\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Pomnožite \sqrt{29} i \sqrt{29} da biste dobili 29.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}+32\sqrt{41}+20\sqrt{5945}-8\times 29\sqrt{41}+4\sqrt{1189}\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Pomnožite -8 i 29 da biste dobili -232.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}+32\sqrt{41}+20\sqrt{5945}-232\sqrt{41}+4\sqrt{1189}\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kombinirajte 32\sqrt{41} i -232\sqrt{41} da biste dobili -200\sqrt{41}.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}-200\sqrt{41}+20\sqrt{5945}+4\sqrt{1189}\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Rastavite 1189=41\times 29 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{41\times 29} kao umnožak kvadrata korijena \sqrt{41}\sqrt{29}.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}-200\sqrt{41}+20\sqrt{5945}+4\sqrt{41}\sqrt{29}\sqrt{41}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Pomnožite \sqrt{41} i \sqrt{41} da biste dobili 41.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}-200\sqrt{41}+20\sqrt{5945}+4\times 41\sqrt{29}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Pomnožite 4 i 41 da biste dobili 164.

$$\sqrt{\frac{\left(160\sqrt{5}-64\sqrt{29}-200\sqrt{41}+20\sqrt{5945}+164\sqrt{29}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Kombinirajte -64\sqrt{29} i 164\sqrt{29} da biste dobili 100\sqrt{29}.

$$\sqrt{\frac{\left(160\sqrt{5}+100\sqrt{29}-200\sqrt{41}+20\sqrt{5945}\right)\left(5\sqrt{5}+2\sqrt{29}-\sqrt{41}\right)}{16}}$$

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza 160\sqrt{5}+100\sqrt{29}-200\sqrt{41}+20\sqrt{5945} sa svakim dijelom izraza 5\sqrt{5}+2\sqrt{29}-\sqrt{41}.

$$\sqrt{\frac{800\left(\sqrt{5}\right)^{2}+320\sqrt{29}\sqrt{5}-160\sqrt{5}\sqrt{41}+500\sqrt{5}\sqrt{29}+200\left(\sqrt{29}\right)^{2}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kvadrat od \sqrt{5} je 5.

$$\sqrt{\frac{800\times 5+320\sqrt{29}\sqrt{5}-160\sqrt{5}\sqrt{41}+500\sqrt{5}\sqrt{29}+200\left(\sqrt{29}\right)^{2}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Pomnožite 800 i 5 da biste dobili 4000.

$$\sqrt{\frac{4000+320\sqrt{29}\sqrt{5}-160\sqrt{5}\sqrt{41}+500\sqrt{5}\sqrt{29}+200\left(\sqrt{29}\right)^{2}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Da biste pomnožite \sqrt{29} i \sqrt{5}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{4000+320\sqrt{145}-160\sqrt{5}\sqrt{41}+500\sqrt{5}\sqrt{29}+200\left(\sqrt{29}\right)^{2}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Da biste pomnožite \sqrt{5} i \sqrt{41}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{4000+320\sqrt{145}-160\sqrt{205}+500\sqrt{5}\sqrt{29}+200\left(\sqrt{29}\right)^{2}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Da biste pomnožite \sqrt{5} i \sqrt{29}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{4000+320\sqrt{145}-160\sqrt{205}+500\sqrt{145}+200\left(\sqrt{29}\right)^{2}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kombinirajte 320\sqrt{145} i 500\sqrt{145} da biste dobili 820\sqrt{145}.

$$\sqrt{\frac{4000+820\sqrt{145}-160\sqrt{205}+200\left(\sqrt{29}\right)^{2}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kvadrat od \sqrt{29} je 29.

$$\sqrt{\frac{4000+820\sqrt{145}-160\sqrt{205}+200\times 29-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Pomnožite 200 i 29 da biste dobili 5800.

$$\sqrt{\frac{4000+820\sqrt{145}-160\sqrt{205}+5800-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Dodajte 4000 broju 5800 da biste dobili 9800.

$$\sqrt{\frac{9800+820\sqrt{145}-160\sqrt{205}-100\sqrt{29}\sqrt{41}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Da biste pomnožite \sqrt{29} i \sqrt{41}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{9800+820\sqrt{145}-160\sqrt{205}-100\sqrt{1189}-1000\sqrt{41}\sqrt{5}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Da biste pomnožite \sqrt{41} i \sqrt{5}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{9800+820\sqrt{145}-160\sqrt{205}-100\sqrt{1189}-1000\sqrt{205}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kombinirajte -160\sqrt{205} i -1000\sqrt{205} da biste dobili -1160\sqrt{205}.

$$\sqrt{\frac{9800+820\sqrt{145}-1160\sqrt{205}-100\sqrt{1189}-400\sqrt{41}\sqrt{29}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Da biste pomnožite \sqrt{41} i \sqrt{29}, pomnožite brojeve u kvadratnim korijenu.

$$\sqrt{\frac{9800+820\sqrt{145}-1160\sqrt{205}-100\sqrt{1189}-400\sqrt{1189}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kombinirajte -100\sqrt{1189} i -400\sqrt{1189} da biste dobili -500\sqrt{1189}.

$$\sqrt{\frac{9800+820\sqrt{145}-1160\sqrt{205}-500\sqrt{1189}+200\left(\sqrt{41}\right)^{2}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kvadrat od \sqrt{41} je 41.

$$\sqrt{\frac{9800+820\sqrt{145}-1160\sqrt{205}-500\sqrt{1189}+200\times 41+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Pomnožite 200 i 41 da biste dobili 8200.

$$\sqrt{\frac{9800+820\sqrt{145}-1160\sqrt{205}-500\sqrt{1189}+8200+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Dodajte 9800 broju 8200 da biste dobili 18000.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}-500\sqrt{1189}+100\sqrt{5945}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Rastavite 5945=5\times 1189 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{5\times 1189} kao umnožak kvadrata korijena \sqrt{5}\sqrt{1189}.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}-500\sqrt{1189}+100\sqrt{5}\sqrt{1189}\sqrt{5}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Pomnožite \sqrt{5} i \sqrt{5} da biste dobili 5.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}-500\sqrt{1189}+100\times 5\sqrt{1189}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Pomnožite 100 i 5 da biste dobili 500.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}-500\sqrt{1189}+500\sqrt{1189}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kombinirajte -500\sqrt{1189} i 500\sqrt{1189} da biste dobili 0.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}+40\sqrt{5945}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Rastavite 5945=29\times 205 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{29\times 205} kao umnožak kvadrata korijena \sqrt{29}\sqrt{205}.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}+40\sqrt{29}\sqrt{205}\sqrt{29}-20\sqrt{41}\sqrt{5945}}{16}}$$

Pomnožite \sqrt{29} i \sqrt{29} da biste dobili 29.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}+40\times 29\sqrt{205}-20\sqrt{41}\sqrt{5945}}{16}}$$

Pomnožite 40 i 29 da biste dobili 1160.

$$\sqrt{\frac{18000+820\sqrt{145}-1160\sqrt{205}+1160\sqrt{205}-20\sqrt{41}\sqrt{5945}}{16}}$$

Kombinirajte -1160\sqrt{205} i 1160\sqrt{205} da biste dobili 0.

$$\sqrt{\frac{18000+820\sqrt{145}-20\sqrt{41}\sqrt{5945}}{16}}$$

Rastavite 5945=41\times 145 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{41\times 145} kao umnožak kvadrata korijena \sqrt{41}\sqrt{145}.

$$\sqrt{\frac{18000+820\sqrt{145}-20\sqrt{41}\sqrt{41}\sqrt{145}}{16}}$$

Pomnožite \sqrt{41} i \sqrt{41} da biste dobili 41.

$$\sqrt{\frac{18000+820\sqrt{145}-20\times 41\sqrt{145}}{16}}$$

Pomnožite -20 i 41 da biste dobili -820.

$$\sqrt{\frac{18000+820\sqrt{145}-820\sqrt{145}}{16}}$$

Kombinirajte 820\sqrt{145} i -820\sqrt{145} da biste dobili 0.

$$\sqrt{\frac{18000}{16}}$$

Podijelite 18000 s 16 da biste dobili 1125.

$$\sqrt{1125}$$

Rastavite 1125=15^{2}\times 5 na faktore. Ponovno napišite kvadratni korijen proizvoda \sqrt{15^{2}\times 5} kao umnožak kvadrata korijena \sqrt{15^{2}}\sqrt{5}. Izračunajte kvadratni korijen od 15^{2}.

$$15\sqrt{5}$$