Solve sqrt{5^211^2sqrt{3^142^10sqrt{{3}^4{2}^4}}}

$$\sqrt{ { 5 }^{ 2 } { 11 }^{ 2 } \sqrt{ { 3 }^{ 14 } { 2 }^{ 10 } \sqrt{ { 3 }^{ 4 } { 2 }^{ 4 } } } }$$

Evaluate

$$35640$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25\times 11^{2}\sqrt{3^{14}\times 2^{10}\sqrt{3^{4}\times 2^{4}}}}$$

Calculate 11 to the power of 2 and get 121.

$$\sqrt{25\times 121\sqrt{3^{14}\times 2^{10}\sqrt{3^{4}\times 2^{4}}}}$$

Multiply 25 and 121 to get 3025.

$$\sqrt{3025\sqrt{3^{14}\times 2^{10}\sqrt{3^{4}\times 2^{4}}}}$$

Calculate 3 to the power of 14 and get 4782969.

$$\sqrt{3025\sqrt{4782969\times 2^{10}\sqrt{3^{4}\times 2^{4}}}}$$

Calculate 2 to the power of 10 and get 1024.

$$\sqrt{3025\sqrt{4782969\times 1024\sqrt{3^{4}\times 2^{4}}}}$$

Multiply 4782969 and 1024 to get 4897760256.

$$\sqrt{3025\sqrt{4897760256\sqrt{3^{4}\times 2^{4}}}}$$

Calculate 3 to the power of 4 and get 81.

$$\sqrt{3025\sqrt{4897760256\sqrt{81\times 2^{4}}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{3025\sqrt{4897760256\sqrt{81\times 16}}}$$

Multiply 81 and 16 to get 1296.

$$\sqrt{3025\sqrt{4897760256\sqrt{1296}}}$$

Calculate the square root of 1296 and get 36.

$$\sqrt{3025\sqrt{4897760256\times 36}}$$

Multiply 4897760256 and 36 to get 176319369216.

$$\sqrt{3025\sqrt{176319369216}}$$

Calculate the square root of 176319369216 and get 419904.

$$\sqrt{3025\times 419904}$$

Multiply 3025 and 419904 to get 1270209600.

$$\sqrt{1270209600}$$

Calculate the square root of 1270209600 and get 35640.

$$35640$$

Factor

$$2^{3}\times 3^{4}\times 5\times 11$$