Solve sqrt{814*25^22}

$$\sqrt{ 814 \times { 25 }^{ 2 } 2 }$$

Evaluate

$$50\sqrt{407}\approx 1008.712050092$$

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$\sqrt{814\times 625\times 2}$$

Multiply 814 and 625 to get 508750.

$$\sqrt{508750\times 2}$$

Multiply 508750 and 2 to get 1017500.

$$\sqrt{1017500}$$

Factor 1017500=50^{2}\times 407. Rewrite the square root of the product \sqrt{50^{2}\times 407} as the product of square roots \sqrt{50^{2}}\sqrt{407}. Take the square root of 50^{2}.

$$50\sqrt{407}$$