Solve {left(2sqrt{5}right)}^2{left(3sqrt{2}right)}^2

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

Evaluate

$$360$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{5}\right)^{2}\times \left(3\sqrt{2}\right)^{2}$$

The square of \sqrt{5} is 5.

$$4\times 5\times \left(3\sqrt{2}\right)^{2}$$

Multiply 4 and 5 to get 20.

$$20\times \left(3\sqrt{2}\right)^{2}$$

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

$$20\times 3^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$20\times 9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$20\times 9\times 2$$

Multiply 9 and 2 to get 18.

$$20\times 18$$

Multiply 20 and 18 to get 360.

$$360$$

Factor

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