Solve sqrt{150^2+1200^2}

$$\sqrt{ { 150 }^{ 2 } + { 1200 }^{ 2 } }$$

Evaluate

$$150\sqrt{65}\approx 1209.338662245$$

Solution Steps

Calculate 150 to the power of 2 and get 22500.

$$\sqrt{22500+1200^{2}}$$

Calculate 1200 to the power of 2 and get 1440000.

$$\sqrt{22500+1440000}$$

Add 22500 and 1440000 to get 1462500.

$$\sqrt{1462500}$$

Factor 1462500=150^{2}\times 65. Rewrite the square root of the product \sqrt{150^{2}\times 65} as the product of square roots \sqrt{150^{2}}\sqrt{65}. Take the square root of 150^{2}.

$$150\sqrt{65}$$