Resolver 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}}=

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

Avaliar

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

Passos Para a Resolução

Multiplique \frac{5\sqrt{5}+2\sqrt{29}+\sqrt{41}}{2} vezes \frac{-5\sqrt{5}+2\sqrt{29}+\sqrt{41}}{2} ao multiplicar o numerador vezes o numerador e o denominador vezes o denominador.

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

Multiplique \frac{\left(5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)\left(-5\sqrt{5}+2\sqrt{29}+\sqrt{41}\right)}{2\times 2} vezes \frac{5\sqrt{5}-2\sqrt{29}+\sqrt{41}}{2} ao multiplicar o numerador vezes o numerador e o denominador vezes o denominador.

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

Multiplique \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} vezes \frac{5\sqrt{5}+2\sqrt{29}-\sqrt{41}}{2} ao multiplicar o numerador vezes o numerador e o denominador vezes o denominador.

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

Multiplique 2 e 2 para obter 4.

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

Multiplique 4 e 2 para obter 8.

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

Multiplique 8 e 2 para obter 16.

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

Aplique a propriedade distributiva ao multiplicar cada termo de 5\sqrt{5}+2\sqrt{29}+\sqrt{41} por cada termo de -5\sqrt{5}+2\sqrt{29}+\sqrt{41}.

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

O quadrado de \sqrt{5} é 5.

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

Multiplique -25 e 5 para obter -125.

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

Para multiplicar \sqrt{29} e \sqrt{5}, multiplique os números sob a raiz quadrada.

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

Para multiplicar \sqrt{5} e \sqrt{41}, multiplique os números sob a raiz quadrada.

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

Para multiplicar \sqrt{5} e \sqrt{29}, multiplique os números sob a raiz quadrada.

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

Combine 10\sqrt{145} e -10\sqrt{145} para obter 0.

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

O quadrado de \sqrt{29} é 29.

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

Multiplique 4 e 29 para obter 116.

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

Some -125 e 116 para obter -9.

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

Para multiplicar \sqrt{29} e \sqrt{41}, multiplique os números sob a raiz quadrada.

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

Para multiplicar \sqrt{41} e \sqrt{5}, multiplique os números sob a raiz quadrada.

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

Combine 5\sqrt{205} e -5\sqrt{205} para obter 0.

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

Para multiplicar \sqrt{41} e \sqrt{29}, multiplique os números sob a raiz quadrada.

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

Combine 2\sqrt{1189} e 2\sqrt{1189} para obter 4\sqrt{1189}.

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

O quadrado de \sqrt{41} é 41.

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

Some -9 e 41 para obter 32.

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

Aplique a propriedade distributiva ao multiplicar cada termo de 32+4\sqrt{1189} por cada termo de 5\sqrt{5}-2\sqrt{29}+\sqrt{41}.

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

Para multiplicar \sqrt{5} e \sqrt{1189}, multiplique os números sob a raiz quadrada.

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

Fatorize a expressão 1189=29\times 41. Reescreva a raiz quadrada do produto \sqrt{29\times 41} à medida que o produto das raízes quadradas \sqrt{29}\sqrt{41}.

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

Multiplique \sqrt{29} e \sqrt{29} para obter 29.

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

Multiplique -8 e 29 para obter -232.

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

Combine 32\sqrt{41} e -232\sqrt{41} para obter -200\sqrt{41}.

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

Fatorize a expressão 1189=41\times 29. Reescreva a raiz quadrada do produto \sqrt{41\times 29} à medida que o produto das raízes quadradas \sqrt{41}\sqrt{29}.

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

Multiplique \sqrt{41} e \sqrt{41} para obter 41.

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

Multiplique 4 e 41 para obter 164.

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

Combine -64\sqrt{29} e 164\sqrt{29} para obter 100\sqrt{29}.

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

Aplique a propriedade distributiva ao multiplicar cada termo de 160\sqrt{5}+100\sqrt{29}-200\sqrt{41}+20\sqrt{5945} por cada termo de 5\sqrt{5}+2\sqrt{29}-\sqrt{41}.

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

O quadrado de \sqrt{5} é 5.

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

Multiplique 800 e 5 para obter 4000.

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

Para multiplicar \sqrt{29} e \sqrt{5}, multiplique os números sob a raiz quadrada.

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

Para multiplicar \sqrt{5} e \sqrt{41}, multiplique os números sob a raiz quadrada.

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

Para multiplicar \sqrt{5} e \sqrt{29}, multiplique os números sob a raiz quadrada.

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

Combine 320\sqrt{145} e 500\sqrt{145} para obter 820\sqrt{145}.

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

O quadrado de \sqrt{29} é 29.

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

Multiplique 200 e 29 para obter 5800.

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

Some 4000 e 5800 para obter 9800.

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

Para multiplicar \sqrt{29} e \sqrt{41}, multiplique os números sob a raiz quadrada.

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

Para multiplicar \sqrt{41} e \sqrt{5}, multiplique os números sob a raiz quadrada.

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

Combine -160\sqrt{205} e -1000\sqrt{205} para obter -1160\sqrt{205}.

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

Para multiplicar \sqrt{41} e \sqrt{29}, multiplique os números sob a raiz quadrada.

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

Combine -100\sqrt{1189} e -400\sqrt{1189} para obter -500\sqrt{1189}.

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

O quadrado de \sqrt{41} é 41.

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

Multiplique 200 e 41 para obter 8200.

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

Some 9800 e 8200 para obter 18000.

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

Fatorize a expressão 5945=5\times 1189. Reescreva a raiz quadrada do produto \sqrt{5\times 1189} à medida que o produto das raízes quadradas \sqrt{5}\sqrt{1189}.

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

Multiplique \sqrt{5} e \sqrt{5} para obter 5.

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

Multiplique 100 e 5 para obter 500.

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

Combine -500\sqrt{1189} e 500\sqrt{1189} para obter 0.

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

Fatorize a expressão 5945=29\times 205. Reescreva a raiz quadrada do produto \sqrt{29\times 205} à medida que o produto das raízes quadradas \sqrt{29}\sqrt{205}.

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

Multiplique \sqrt{29} e \sqrt{29} para obter 29.

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

Multiplique 40 e 29 para obter 1160.

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

Combine -1160\sqrt{205} e 1160\sqrt{205} para obter 0.

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

Fatorize a expressão 5945=41\times 145. Reescreva a raiz quadrada do produto \sqrt{41\times 145} à medida que o produto das raízes quadradas \sqrt{41}\sqrt{145}.

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

Multiplique \sqrt{41} e \sqrt{41} para obter 41.

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

Multiplique -20 e 41 para obter -820.

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

Combine 820\sqrt{145} e -820\sqrt{145} para obter 0.

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

Dividir 18000 por 16 para obter 1125.

$$\sqrt{1125}$$

Fatorize a expressão 1125=15^{2}\times 5. Reescreva a raiz quadrada do produto \sqrt{15^{2}\times 5} à medida que o produto das raízes quadradas \sqrt{15^{2}}\sqrt{5}. Calcule a raiz quadrada de 15^{2}.

$$15\sqrt{5}$$