Solve sqrt{3^28^2sqrt{7^42^4sqrt{{10}^8{5}^8}}}

$$\sqrt{ { 3 }^{ 2 } { 8 }^{ 2 } \sqrt{ { 7 }^{ 4 } { 2 }^{ 4 } \sqrt{ { 10 }^{ 8 } { 5 }^{ 8 } } } }$$

Evaluate

$$16800$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\times 8^{2}\sqrt{7^{4}\times 2^{4}\sqrt{10^{8}\times 5^{8}}}}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt{9\times 64\sqrt{7^{4}\times 2^{4}\sqrt{10^{8}\times 5^{8}}}}$$

Multiply 9 and 64 to get 576.

$$\sqrt{576\sqrt{7^{4}\times 2^{4}\sqrt{10^{8}\times 5^{8}}}}$$

Calculate 7 to the power of 4 and get 2401.

$$\sqrt{576\sqrt{2401\times 2^{4}\sqrt{10^{8}\times 5^{8}}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{576\sqrt{2401\times 16\sqrt{10^{8}\times 5^{8}}}}$$

Multiply 2401 and 16 to get 38416.

$$\sqrt{576\sqrt{38416\sqrt{10^{8}\times 5^{8}}}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\sqrt{576\sqrt{38416\sqrt{100000000\times 5^{8}}}}$$

Calculate 5 to the power of 8 and get 390625.

$$\sqrt{576\sqrt{38416\sqrt{100000000\times 390625}}}$$

Multiply 100000000 and 390625 to get 39062500000000.

$$\sqrt{576\sqrt{38416\sqrt{39062500000000}}}$$

Calculate the square root of 39062500000000 and get 6250000.

$$\sqrt{576\sqrt{38416\times 6250000}}$$

Multiply 38416 and 6250000 to get 240100000000.

$$\sqrt{576\sqrt{240100000000}}$$

Calculate the square root of 240100000000 and get 490000.

$$\sqrt{576\times 490000}$$

Multiply 576 and 490000 to get 282240000.

$$\sqrt{282240000}$$

Calculate the square root of 282240000 and get 16800.

$$16800$$

Factor

$$2^{5}\times 3\times 5^{2}\times 7$$