Solve 1/2[(3/5)^2+(3/5)^2+(1/2)^2]=

$$\frac { 1 } { 2 } [ ( \frac { 3 } { 5 } ) ^ { 2 } + ( \frac { 3 } { 5 } ) ^ { 2 } + ( \frac { 1 } { 2 } ) ^ { 2 } ] =$$

Evaluate

$$\frac{97}{200}=0.485$$

Solution Steps

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{1}{2}\left(\frac{9}{25}+\left(\frac{3}{5}\right)^{2}+\left(\frac{1}{2}\right)^{2}\right)$$

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{1}{2}\left(\frac{9}{25}+\frac{9}{25}+\left(\frac{1}{2}\right)^{2}\right)$$

Since \frac{9}{25} and \frac{9}{25} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\left(\frac{9+9}{25}+\left(\frac{1}{2}\right)^{2}\right)$$

Add 9 and 9 to get 18.

$$\frac{1}{2}\left(\frac{18}{25}+\left(\frac{1}{2}\right)^{2}\right)$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{2}\left(\frac{18}{25}+\frac{1}{4}\right)$$

Least common multiple of 25 and 4 is 100. Convert \frac{18}{25} and \frac{1}{4} to fractions with denominator 100.

$$\frac{1}{2}\left(\frac{72}{100}+\frac{25}{100}\right)$$

Since \frac{72}{100} and \frac{25}{100} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\times \frac{72+25}{100}$$

Add 72 and 25 to get 97.

$$\frac{1}{2}\times \frac{97}{100}$$

Multiply \frac{1}{2} times \frac{97}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 97}{2\times 100}$$

Do the multiplications in the fraction \frac{1\times 97}{2\times 100}.

$$\frac{97}{200}$$

Factor

$$\frac{97}{2 ^ {3} \cdot 5 ^ {2}} = 0.485$$