Solve sqrt{18^2-(6sqrt{5})^2}

$$\sqrt { 18 ^ { 2 } - ( 6 \sqrt { 5 } ) ^ { 2 } }$$

Evaluate

$$12$$

Solution Steps

Calculate 18 to the power of 2 and get 324.

$$\sqrt{324-\left(6\sqrt{5}\right)^{2}}$$

Expand \left(6\sqrt{5}\right)^{2}.

$$\sqrt{324-6^{2}\left(\sqrt{5}\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{324-36\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{324-36\times 5}$$

Multiply 36 and 5 to get 180.

$$\sqrt{324-180}$$

Subtract 180 from 324 to get 144.

$$\sqrt{144}$$

Calculate the square root of 144 and get 12.

$$12$$

Factor

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