Solve sqrt{53^3+8}+frac{sqrt{72}}{456}

$$\sqrt { 53 ^ { 3 } + 8 } + \frac { \sqrt { 72 } } { 456 }$$

Evaluate

$$\frac{\sqrt{2}}{76}+\sqrt{148885}\approx 385.874798901$$

Solution Steps

Calculate 53 to the power of 3 and get 148877.

$$\sqrt{148877+8}+\frac{\sqrt{72}}{456}$$

Add 148877 and 8 to get 148885.

$$\sqrt{148885}+\frac{\sqrt{72}}{456}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\sqrt{148885}+\frac{6\sqrt{2}}{456}$$

Divide 6\sqrt{2} by 456 to get \frac{1}{76}\sqrt{2}.

$$\sqrt{148885}+\frac{1}{76}\sqrt{2}$$

Factor

$$\frac{\sqrt{2} + 76 \sqrt{148885}}{76} = 385.87479890080823$$