Solve {left(1.8sqrt{3}right)}^2-{left(frac{1.8sqrt{3}}{2}right)}^2

$${ \left(1.8 \sqrt{ 3 } \right) }^{ 2 } - { \left( \frac{ 1.8 \sqrt{ 3 } }{ 2 } \right) }^{ 2 }$$

Evaluate

$$7.29$$

Solution Steps

Expand \left(1.8\sqrt{3}\right)^{2}.

$$1.8^{2}\left(\sqrt{3}\right)^{2}-\left(\frac{1.8\sqrt{3}}{2}\right)^{2}$$

Calculate 1.8 to the power of 2 and get 3.24.

$$3.24\left(\sqrt{3}\right)^{2}-\left(\frac{1.8\sqrt{3}}{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$3.24\times 3-\left(\frac{1.8\sqrt{3}}{2}\right)^{2}$$

Multiply 3.24 and 3 to get 9.72.

$$9.72-\left(\frac{1.8\sqrt{3}}{2}\right)^{2}$$

Divide 1.8\sqrt{3} by 2 to get 0.9\sqrt{3}.

$$9.72-\left(0.9\sqrt{3}\right)^{2}$$

Expand \left(0.9\sqrt{3}\right)^{2}.

$$9.72-0.9^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 0.9 to the power of 2 and get 0.81.

$$9.72-0.81\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$9.72-0.81\times 3$$

Multiply 0.81 and 3 to get 2.43.

$$9.72-2.43$$

Subtract 2.43 from 9.72 to get 7.29.

$$7.29$$

Factor

$$\frac{3 ^ {6}}{2 ^ {2} \cdot 5 ^ {2}} = 7\frac{29}{100} = 7.29$$