Solve 3^2/2^2+frac{{left(3sqrt{2}right)}^2}{2^2}

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

Evaluate

$$\frac{27}{4}=6.75$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{2^{2}}+\frac{\left(3\sqrt{2}\right)^{2}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9}{4}+\frac{\left(3\sqrt{2}\right)^{2}}{2^{2}}$$

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

$$\frac{9}{4}+\frac{3^{2}\left(\sqrt{2}\right)^{2}}{2^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{4}+\frac{9\left(\sqrt{2}\right)^{2}}{2^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{9}{4}+\frac{9\times 2}{2^{2}}$$

Multiply 9 and 2 to get 18.

$$\frac{9}{4}+\frac{18}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9}{4}+\frac{18}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{4}+\frac{9}{2}$$

Add \frac{9}{4} and \frac{9}{2} to get \frac{27}{4}.

$$\frac{27}{4}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2}} = 6\frac{3}{4} = 6.75$$