Solve 5145sqrt{4sqrt{15^254^24^2/5^2}}

$$5145 \sqrt{ 4 \sqrt{ { 15 }^{ 2 } { 54 }^{ 2 } \frac{ { 4 }^{ 2 } }{ { 5 }^{ 2 } } } }$$

Evaluate

$$185220\sqrt{2}\approx 261940.636022745$$

Solution Steps

Calculate 15 to the power of 2 and get 225.

$$5145\sqrt{4\sqrt{225\times 54^{2}\times \frac{4^{2}}{5^{2}}}}$$

Calculate 54 to the power of 2 and get 2916.

$$5145\sqrt{4\sqrt{225\times 2916\times \frac{4^{2}}{5^{2}}}}$$

Multiply 225 and 2916 to get 656100.

$$5145\sqrt{4\sqrt{656100\times \frac{4^{2}}{5^{2}}}}$$

Calculate 4 to the power of 2 and get 16.

$$5145\sqrt{4\sqrt{656100\times \frac{16}{5^{2}}}}$$

Calculate 5 to the power of 2 and get 25.

$$5145\sqrt{4\sqrt{656100\times \frac{16}{25}}}$$

Express 656100\times \frac{16}{25} as a single fraction.

$$5145\sqrt{4\sqrt{\frac{656100\times 16}{25}}}$$

Multiply 656100 and 16 to get 10497600.

$$5145\sqrt{4\sqrt{\frac{10497600}{25}}}$$

Divide 10497600 by 25 to get 419904.

$$5145\sqrt{4\sqrt{419904}}$$

Calculate the square root of 419904 and get 648.

$$5145\sqrt{4\times 648}$$

Multiply 4 and 648 to get 2592.

$$5145\sqrt{2592}$$

Factor 2592=36^{2}\times 2. Rewrite the square root of the product \sqrt{36^{2}\times 2} as the product of square roots \sqrt{36^{2}}\sqrt{2}. Take the square root of 36^{2}.

$$5145\times 36\sqrt{2}$$

Multiply 5145 and 36 to get 185220.

$$185220\sqrt{2}$$