Solve sqrt{{left(300sqrt{3}right)}^2+300^2}

$$\sqrt{ { \left(300 \sqrt{ 3 } \right) }^{ 2 } + { 300 }^{ 2 } }$$

Evaluate

$$600$$

Solution Steps

Expand \left(300\sqrt{3}\right)^{2}.

$$\sqrt{300^{2}\left(\sqrt{3}\right)^{2}+300^{2}}$$

Calculate 300 to the power of 2 and get 90000.

$$\sqrt{90000\left(\sqrt{3}\right)^{2}+300^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{90000\times 3+300^{2}}$$

Multiply 90000 and 3 to get 270000.

$$\sqrt{270000+300^{2}}$$

Calculate 300 to the power of 2 and get 90000.

$$\sqrt{270000+90000}$$

Add 270000 and 90000 to get 360000.

$$\sqrt{360000}$$

Calculate the square root of 360000 and get 600.

$$600$$

Factor

$$2^{3}\times 3\times 5^{2}$$