Solve frac{sqrt{3860^2+1440^2}}{27}

$$\frac{ \sqrt{ { 3860 }^{ 2 } + { 1440 }^{ 2 } } }{ 27 }$$

Evaluate

$$\frac{20\sqrt{42433}}{27}\approx 152.587198754$$

Solution Steps

Calculate 3860 to the power of 2 and get 14899600.

$$\frac{\sqrt{14899600+1440^{2}}}{27}$$

Calculate 1440 to the power of 2 and get 2073600.

$$\frac{\sqrt{14899600+2073600}}{27}$$

Add 14899600 and 2073600 to get 16973200.

$$\frac{\sqrt{16973200}}{27}$$

Factor 16973200=20^{2}\times 42433. Rewrite the square root of the product \sqrt{20^{2}\times 42433} as the product of square roots \sqrt{20^{2}}\sqrt{42433}. Take the square root of 20^{2}.

$$\frac{20\sqrt{42433}}{27}$$