Solve sqrt{60^2-(30sqrt{3})^2}=

$$\sqrt { 60 ^ { 2 } - ( 30 \sqrt { 3 } ) ^ { 2 } } =$$

Evaluate

$$30$$

Solution Steps

Calculate 60 to the power of 2 and get 3600.

$$\sqrt{3600-\left(30\sqrt{3}\right)^{2}}$$

Expand \left(30\sqrt{3}\right)^{2}.

$$\sqrt{3600-30^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate 30 to the power of 2 and get 900.

$$\sqrt{3600-900\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{3600-900\times 3}$$

Multiply 900 and 3 to get 2700.

$$\sqrt{3600-2700}$$

Subtract 2700 from 3600 to get 900.

$$\sqrt{900}$$

Calculate the square root of 900 and get 30.

$$30$$

Factor

$$2\times 3\times 5$$