Solve sqrt{1024^2+600^2}div7

$$\sqrt{ { 1024 }^{ 2 } + { 600 }^{ 2 } } \div 7$$

Evaluate

$$\frac{8\sqrt{22009}}{7}\approx 169.547777867$$

Solution Steps

Calculate 1024 to the power of 2 and get 1048576.

$$\frac{\sqrt{1048576+600^{2}}}{7}$$

Calculate 600 to the power of 2 and get 360000.

$$\frac{\sqrt{1048576+360000}}{7}$$

Add 1048576 and 360000 to get 1408576.

$$\frac{\sqrt{1408576}}{7}$$

Factor 1408576=8^{2}\times 22009. Rewrite the square root of the product \sqrt{8^{2}\times 22009} as the product of square roots \sqrt{8^{2}}\sqrt{22009}. Take the square root of 8^{2}.

$$\frac{8\sqrt{22009}}{7}$$