Solve sqrt{(200sqrt{3})^2+600^2}=

$$\sqrt { ( 200 \sqrt { 3 } ) ^ { 2 } + 600 ^ { 2 } } =$$

Evaluate

$$400\sqrt{3}\approx 692.820323028$$

Solution Steps

Expand \left(200\sqrt{3}\right)^{2}.

$$\sqrt{200^{2}\left(\sqrt{3}\right)^{2}+600^{2}}$$

Calculate 200 to the power of 2 and get 40000.

$$\sqrt{40000\left(\sqrt{3}\right)^{2}+600^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{40000\times 3+600^{2}}$$

Multiply 40000 and 3 to get 120000.

$$\sqrt{120000+600^{2}}$$

Calculate 600 to the power of 2 and get 360000.

$$\sqrt{120000+360000}$$

Add 120000 and 360000 to get 480000.

$$\sqrt{480000}$$

Factor 480000=400^{2}\times 3. Rewrite the square root of the product \sqrt{400^{2}\times 3} as the product of square roots \sqrt{400^{2}}\sqrt{3}. Take the square root of 400^{2}.

$$400\sqrt{3}$$