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

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

Evaluate

$$5$$

Solution Steps

To raise \frac{3\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Since \frac{\left(3\sqrt{2}\right)^{2}}{2^{2}} and \frac{\left(\sqrt{2}\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

The square of \sqrt{2} is 2.

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

Multiply 9 and 2 to get 18.

$$\frac{18}{2^{2}}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{18}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}$$

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

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

The square of \sqrt{2} is 2.

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

Calculate 2 to the power of 2 and get 4.

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

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

$$\frac{9}{2}+\frac{1}{2}$$

Add \frac{9}{2} and \frac{1}{2} to get 5.

$$5$$

Factor

$$5$$