Solve (5sqrt{3})^2-8(sqrt{2})^2

$$( 5 \sqrt { 3 } ) ^ { 2 } - 8 ( \sqrt { 2 } ) ^ { 2 }$$

Evaluate

$$59$$

Solution Steps

Expand \left(5\sqrt{3}\right)^{2}.

$$5^{2}\left(\sqrt{3}\right)^{2}-8\left(\sqrt{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{3}\right)^{2}-8\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$25\times 3-8\left(\sqrt{2}\right)^{2}$$

Multiply 25 and 3 to get 75.

$$75-8\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$75-8\times 2$$

Multiply 8 and 2 to get 16.

$$75-16$$

Subtract 16 from 75 to get 59.

$$59$$

Factor

$$59$$