Solve (5sqrt{2})^2-3(sqrt{6})^2

$$( 5 \sqrt { 2 } ) ^ { 2 } - 3 ( \sqrt { 6 } ) ^ { 2 }$$

Evaluate

$$32$$

Solution Steps

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

$$5^{2}\left(\sqrt{2}\right)^{2}-3\left(\sqrt{6}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{2}\right)^{2}-3\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{2} is 2.

$$25\times 2-3\left(\sqrt{6}\right)^{2}$$

Multiply 25 and 2 to get 50.

$$50-3\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$50-3\times 6$$

Multiply 3 and 6 to get 18.

$$50-18$$

Subtract 18 from 50 to get 32.

$$32$$

Factor

$$2^{5}$$